さまざまな言語で数値計算

ルンゲ・クッタ・ギル法

初期値 $ x_0 $ から次の式によって, 順次 $ x_1, x_2, \dots $ を求める.

例題として, 初速 $ 250 \mathrm{km/h}, 45^\circ $ の角度で打ったボールの軌跡を, ルンゲ・クッタ・ギル法で計算する
(空気抵抗係数を 0.01 で計算)

本来は一時変数をうまく使って, 必要なメモリを少なく抑えるためのアルゴリズムらしいが,
今回はそこまでやらない.

重力による鉛直方向の減速分は, 重力加速度を $g$, 時間を $t$ とすると,

空気抵抗による水平方向の減速分は,速度を $v$, 速度の水平方向成分を $vx$, 空気抵抗係数を $k$ とすると,

同様に, 鉛直方向の減速分は, 速度の鉛直方向成分を $vy$ とすると,

VBScript

Option Explicit

Private Const PI = 3.14159265359

'重力加速度
Private Const g = -9.8
'空気抵抗係数
Private Const k = -0.01
'時間間隔(秒)
Private Const h = 0.01

'角度
Private Const degree = 45
Private radian: radian = degree * PI / 180.0
'初速 250 km/h -> 秒速に変換
Private v: v = 250 * 1000 \ 3600
'水平方向の速度
Private vx(): ReDim vx(5)
vx(0) = v * Cos(radian)
'鉛直方向の速度
Private vy(): ReDim vy(5)
vy(0) = v * Sin(radian)
'経過秒数
Private t: t = 0.0
'位置
Private x(): ReDim x(5)
x(0) = 0.0
Private y(): ReDim y(5)
y(0) = 0.0

'空気抵抗による水平方向の減速分
Private Function fx(ByVal vx, ByVal vy)
    fx = k * Sqr(vx * vx + vy * vy) * vx
End Function

'重力と空気抵抗による鉛直方向の減速分
Private Function fy(ByVal vx, ByVal vy)
    fy = g + (k * Sqr(vx * vx + vy * vy) * vy)
End Function

'Runge-Kutta-Gill法
Dim i: i = 1
Do While (y(0) >= 0.0)
    '経過秒数
    t = i * h

    '位置・速度
    x(1)  = h *    vx(0)
    y(1)  = h *    vy(0)
    vx(1) = h * fx(vx(0), vy(0))
    vy(1) = h * fy(vx(0), vy(0))

    Dim wx: wx = vx(0) + vx(1) / 2.0
    Dim wy: wy = vy(0) + vy(1) / 2.0
    x(2)  = h *    wx
    y(2)  = h *    wy
    vx(2) = h * fx(wx, wy)
    vy(2) = h * fy(wx, wy)

    wx    = vx(0) + vx(1) * ((Sqr(2.0) - 1) / 2) + vx(2) * (1 - 1 / Sqr(2.0))
    wy    = vy(0) + vy(1) * ((Sqr(2.0) - 1) / 2) + vy(2) * (1 - 1 / Sqr(2.0))
    x(3)  = h *    wx
    y(3)  = h *    wy
    vx(3) = h * fx(wx, wy)
    vy(3) = h * fy(wx, wy)

    wx    = vx(0) - vx(2) / Sqr(2.0) + vx(3) * (1 + 1 / Sqr(2.0))
    wy    = vy(0) - vy(2) / Sqr(2.0) + vy(3) * (1 + 1 / Sqr(2.0))
    x(4)  = h *    wx
    y(4)  = h *    wy
    vx(4) = h * fx(wx, wy)
    vy(4) = h * fy(wx, wy)

    x(0)  = x(0)  + ( x(1) +  x(2) * (2 - Sqr(2.0)) +  x(3) * (2 + Sqr(2.0)) +  x(4)) / 6
    y(0)  = y(0)  + ( y(1) +  y(2) * (2 - Sqr(2.0)) +  y(3) * (2 + Sqr(2.0)) +  y(4)) / 6
    vx(0) = vx(0) + (vx(1) + vx(2) * (2 - Sqr(2.0)) + vx(3) * (2 + Sqr(2.0)) + vx(4)) / 6
    vy(0) = vy(0) + (vy(1) + vy(2) * (2 - Sqr(2.0)) + vy(3) * (2 + Sqr(2.0)) + vy(4)) / 6

    WScript.StdOut.Write     Right(Space(4) & FormatNumber(t,     2, -1, 0, 0), 4) & vbTab
    WScript.StdOut.Write     Right(Space(8) & FormatNumber(vx(0), 5, -1, 0, 0), 8) & vbTab
    WScript.StdOut.Write     Right(Space(9) & FormatNumber(vy(0), 5, -1, 0, 0), 9) & vbTab
    WScript.StdOut.Write     Right(Space(9) & FormatNumber(x(0),  5, -1, 0, 0), 9) & vbTab
    WScript.StdOut.WriteLine Right(Space(9) & FormatNumber(y(0),  5, -1, 0, 0), 9)

    i = i + 1
Loop

Z:\>cscript //nologo Z:\0805.vbs
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

JScript

// 重力加速度
var g = -9.8
// 空気抵抗係数
var k = -0.01
// 時間間隔(秒)
var h = 0.01

// 角度
var degree = 45
var radian = degree * Math.PI / 180.0
// 初速 250 km/h -> 秒速に変換
var v = parseInt(250 * 1000 / 3600)
// 水平方向の速度
var vx = []
vx[0] = v * Math.cos(radian)
// 鉛直方向の速度
var vy = []
vy[0] = v * Math.sin(radian)
// 経過秒数
var t = 0.0
// 位置
var x = []
x[0] = 0.0
var y = []
y[0] = 0.0

// Runge-Kutta-Gill法
for (var i = 1; y[0] >= 0.0; i++)
{
    // 経過秒数
    t = i * h

    // 位置・速度
    x[1]  = h *    vx[0]
    y[1]  = h *    vy[0]
    vx[1] = h * fx(vx[0], vy[0])
    vy[1] = h * fy(vx[0], vy[0])

    var wx = vx[0] + vx[1] / 2
    var wy = vy[0] + vy[1] / 2
    x[2]  = h *    wx
    y[2]  = h *    wy
    vx[2] = h * fx(wx, wy)
    vy[2] = h * fy(wx, wy)

    wx    = vx[0] + vx[1] * ((Math.sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / Math.sqrt(2.0))
    wy    = vy[0] + vy[1] * ((Math.sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / Math.sqrt(2.0))
    x[3]  = h *    wx
    y[3]  = h *    wy
    vx[3] = h * fx(wx, wy)
    vy[3] = h * fy(wx, wy)

    wx    = vx[0] - vx[2] / Math.sqrt(2.0) + vx[3] * (1 + 1 / Math.sqrt(2.0))
    wy    = vy[0] - vy[2] / Math.sqrt(2.0) + vy[3] * (1 + 1 / Math.sqrt(2.0))
    x[4]  = h *    wx
    y[4]  = h *    wy
    vx[4] = h * fx(wx, wy)
    vy[4] = h * fy(wx, wy)

    x[0]  += ( x[1] +  x[2] * (2 - Math.sqrt(2.0)) +  x[3] * (2 + Math.sqrt(2.0)) +  x[4]) / 6
    y[0]  += ( y[1] +  y[2] * (2 - Math.sqrt(2.0)) +  y[3] * (2 + Math.sqrt(2.0)) +  y[4]) / 6
    vx[0] += (vx[1] + vx[2] * (2 - Math.sqrt(2.0)) + vx[3] * (2 + Math.sqrt(2.0)) + vx[4]) / 6
    vy[0] += (vy[1] + vy[2] * (2 - Math.sqrt(2.0)) + vy[3] * (2 + Math.sqrt(2.0)) + vy[4]) / 6

    WScript.StdOut.Write(("    "      + t.toFixed(2)       ).slice(-4) + "\t")
    WScript.StdOut.Write(("        "  + vx[0].toFixed(5)   ).slice(-8) + "\t")
    WScript.StdOut.Write(("         " + vy[0].toFixed(5)   ).slice(-9) + "\t")
    WScript.StdOut.Write(("         " +  x[0].toFixed(5)   ).slice(-9) + "\t")
    WScript.StdOut.Write(("        "  +  y[0].toFixed(5)   ).slice(-8) + "\n")
}

// 空気抵抗による水平方向の減速分
function fx(vx, vy)
{
    return k * Math.sqrt(vx * vx + vy * vy) * vx
}
// 重力と空気抵抗による鉛直方向の減速分
function fy(vx, vy)
{
    return g + (k * Math.sqrt(vx * vx + vy * vy) * vy)
}

Z:\>cscript //nologo Z:\0805.js
0.01    48.45619     48.35852     0.48623    0.48574
0.02    48.12689     47.93222     0.96914    0.96719
0.03    47.80236     47.51133     1.44878    1.44440
0.04    47.48250     47.09575     1.92520    1.91743
0.05    47.16722     46.68537     2.39845    2.38633
0.06    46.85642     46.28007     2.86856    2.85116
0.07    46.55001     45.87974     3.33559    3.31195
0.08    46.24790     45.48430     3.79958    3.76877
0.09    45.94999     45.09363     4.26056    4.22165
省略
6.20     9.25063    -23.74826   125.74997    2.41410
6.21     9.22707    -23.78565   125.84236    2.17643
6.22     9.20355    -23.82289   125.93451    1.93839
6.23     9.18006    -23.85997   126.02643    1.69997
6.24     9.15661    -23.89690   126.11811    1.46119
6.25     9.13319    -23.93366   126.20956    1.22203
6.26     9.10982    -23.97027   126.30078    0.98251
6.27     9.08647    -24.00673   126.39176    0.74263
6.28     9.06317    -24.04303   126.48251    0.50238
6.29     9.03990    -24.07917   126.57302    0.26177
6.30     9.01667    -24.11516   126.66330    0.02080
6.31     8.99347    -24.15100   126.75335   -0.22053

PowerShell

# 重力加速度
$g = -9.8
# 空気抵抗係数
$k = -0.01
# 時間間隔(秒)
$h = 0.01

# 角度
$degree = 45
$radian = $degree * [Math]::PI / 180.0
# 初速 250 km/h -> 秒速に変換
$v = [Math]::Floor(250 * 1000 / 3600)
# 水平方向の速度
$vx  = New-Object double[] 5
$vx[0] = $v * [Math]::Cos($radian)
# 鉛直方向の速度
$vy  = New-Object double[] 5
$vy[0] = $v * [Math]::Sin($radian)
# 経過秒数
$t = 0.0
# 位置
$x  = New-Object double[] 5
$y  = New-Object double[] 5
$x[0] = 0.0
$y[0] = 0.0

# 空気抵抗による水平方向の減速分
function fx($vx, $vy)
{
    return $global:k * [Math]::Sqrt($vx * $vx + $vy * $vy) * $vx
}
# 重力と空気抵抗による鉛直方向の減速分
function fy($vx, $vy)
{
    return $global:g + ($global:k * [Math]::Sqrt($vx * $vx + $vy * $vy) * $vy)
}

# Runge-Kutta-Gill法
for ($i = 1; $y[0] -ge 0.0; $i++)
{
    # 経過秒数
    $t = $i * $h

    # 位置・速度
    $x[1]  = $h *     $vx[0]
    $y[1]  = $h *     $vy[0]
    $vx[1] = $h * (fx $vx[0] $vy[0])
    $vy[1] = $h * (fy $vx[0] $vy[0])

    $wx = $vx[0] + $vx[1] / 2
    $wy = $vy[0] + $vy[1] / 2
    $x[2]  = $h *     $wx
    $y[2]  = $h *     $wy
    $vx[2] = $h * (fx $wx $wy)
    $vy[2] = $h * (fy $wx $wy)

    $wx    = $vx[0] + $vx[1] * (([Math]::Sqrt(2.0) - 1) / 2) + $vx[2] * (1 - 1 / [Math]::Sqrt(2.0))
    $wy    = $vy[0] + $vy[1] * (([Math]::Sqrt(2.0) - 1) / 2) + $vy[2] * (1 - 1 / [Math]::Sqrt(2.0))
    $x[3]  = $h *     $wx
    $y[3]  = $h *     $wy
    $vx[3] = $h * (fx $wx $wy)
    $vy[3] = $h * (fy $wx $wy)

    $wx    = $vx[0] - $vx[2] / [Math]::Sqrt(2.0) + $vx[3] * (1 + 1 / [Math]::Sqrt(2.0))
    $wy    = $vy[0] - $vy[2] / [Math]::Sqrt(2.0) + $vy[3] * (1 + 1 / [Math]::Sqrt(2.0))
    $x[4]  = $h *    $wx
    $y[4]  = $h *    $wy
    $vx[4] = $h * (fx $wx $wy)
    $vy[4] = $h * (fy $wx $wy)

    $x[0]  += ( $x[1] +  $x[2] * (2 - [Math]::Sqrt(2.0)) +  $x[3] * (2 + [Math]::Sqrt(2.0)) +  $x[4]) / 6
    $y[0]  += ( $y[1] +  $y[2] * (2 - [Math]::Sqrt(2.0)) +  $y[3] * (2 + [Math]::Sqrt(2.0)) +  $y[4]) / 6
    $vx[0] += ($vx[1] + $vx[2] * (2 - [Math]::Sqrt(2.0)) + $vx[3] * (2 + [Math]::Sqrt(2.0)) + $vx[4]) / 6
    $vy[0] += ($vy[1] + $vy[2] * (2 - [Math]::Sqrt(2.0)) + $vy[3] * (2 + [Math]::Sqrt(2.0)) + $vy[4]) / 6

    Write-Host ([String]::Format("{0,4:F2}`t{1,8:F5}`t{2,9:F5}`t{3,9:F5}`t{4,8:F5}", $t, $vx[0], $vy[0], $x[0], $y[0]))
}

Z:\>powershell -file Z:\0805.ps1
0.01    48.45619     48.35852     0.48623    0.48574
0.02    48.12689     47.93222     0.96914    0.96719
0.03    47.80236     47.51133     1.44878    1.44440
0.04    47.48250     47.09575     1.92520    1.91743
0.05    47.16722     46.68537     2.39845    2.38633
0.06    46.85642     46.28007     2.86856    2.85116
0.07    46.55001     45.87974     3.33559    3.31195
0.08    46.24790     45.48430     3.79958    3.76877
0.09    45.94999     45.09363     4.26056    4.22165
省略
6.20     9.25063    -23.74826   125.74997    2.41410
6.21     9.22707    -23.78565   125.84236    2.17643
6.22     9.20355    -23.82289   125.93451    1.93839
6.23     9.18006    -23.85997   126.02643    1.69997
6.24     9.15661    -23.89690   126.11811    1.46119
6.25     9.13319    -23.93366   126.20956    1.22203
6.26     9.10982    -23.97027   126.30078    0.98251
6.27     9.08647    -24.00673   126.39176    0.74263
6.28     9.06317    -24.04303   126.48251    0.50238
6.29     9.03990    -24.07917   126.57302    0.26177
6.30     9.01667    -24.11516   126.66330    0.02080
6.31     8.99347    -24.15100   126.75335   -0.22053

Perl

use Math::Trig 'pi';

# 重力加速度
my $g = -9.8;
# 空気抵抗係数
my $k = -0.01;
# 時間間隔(秒)
my $h = 0.01;

# 角度
my $degree = 45;
my $radian = $degree * pi / 180.0;
# 初速 250 km/h -> 秒速に変換
my $v = int(250 * 1000 / 3600);
# 水平方向の速度
my @vx = ();
$vx[0] = $v * cos($radian);
# 鉛直方向の速度
my @vy = ();
$vy[0] = $v * sin($radian);
# 経過秒数
my $t = 0.0;
# 位置
my @x = ();
$x[0] = 0.0;
my @y = ();
$y[0] = 0.0;

# Runge-Kutta-Gill法
for (my $i = 1; $y[0] >= 0.0; $i++)
{
    # 経過秒数
    $t = $i * $h;

    # 位置・速度
    $x[1]  = $h *    $vx[0];
    $y[1]  = $h *    $vy[0];
    $vx[1] = $h * fx($vx[0], $vy[0]);
    $vy[1] = $h * fy($vx[0], $vy[0]);

    my $wx = $vx[0] + $vx[1] / 2;
    my $wy = $vy[0] + $vy[1] / 2;
    $x[2]  = $h *    $wx;
    $y[2]  = $h *    $wy;
    $vx[2] = $h * fx($wx, $wy);
    $vy[2] = $h * fy($wx, $wy);

    $wx    = $vx[0] + $vx[1] * ((sqrt(2.0) - 1) / 2) + $vx[2] * (1 - 1 / sqrt(2.0));
    $wy    = $vy[0] + $vy[1] * ((sqrt(2.0) - 1) / 2) + $vy[2] * (1 - 1 / sqrt(2.0));
    $x[3]  = $h *    $wx;
    $y[3]  = $h *    $wy;
    $vx[3] = $h * fx($wx, $wy);
    $vy[3] = $h * fy($wx, $wy);

    $wx    = $vx[0] - $vx[2] / sqrt(2.0) + $vx[3] * (1 + 1 / sqrt(2.0));
    $wy    = $vy[0] - $vy[2] / sqrt(2.0) + $vy[3] * (1 + 1 / sqrt(2.0));
    $x[4]  = $h *    $wx;
    $y[4]  = $h *    $wy;
    $vx[4] = $h * fx($wx, $wy);
    $vy[4] = $h * fy($wx, $wy);

    $x[0]  += ( $x[1] +  $x[2] * (2 - sqrt(2.0)) +  $x[3] * (2 + sqrt(2.0)) +  $x[4]) / 6;
    $y[0]  += ( $y[1] +  $y[2] * (2 - sqrt(2.0)) +  $y[3] * (2 + sqrt(2.0)) +  $y[4]) / 6;
    $vx[0] += ($vx[1] + $vx[2] * (2 - sqrt(2.0)) + $vx[3] * (2 + sqrt(2.0)) + $vx[4]) / 6;
    $vy[0] += ($vy[1] + $vy[2] * (2 - sqrt(2.0)) + $vy[3] * (2 + sqrt(2.0)) + $vy[4]) / 6;

    printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", $t, $vx[0], $vy[0], $x[0], $y[0]);
}

# 空気抵抗による水平方向の減速分
sub fx
{
  my ($vx, $vy) = @_;
    $k * sqrt($vx * $vx + $vy * $vy) * $vx;
}
# 重力と空気抵抗による鉛直方向の減速分
sub fy
{
    my ($vx, $vy) = @_;
    $g + ($k * sqrt($vx * $vx + $vy * $vy) * $vy);
}

Z:\>perl Z:\0805.pl
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

PHP

<?php

# 重力加速度
$g = -9.8;
# 空気抵抗係数
$k = -0.01;
# 時間間隔(秒)
$h = 0.01;

# 角度
$degree = 45;
$radian = $degree * M_PI / 180.0;
# 初速 250 km/h -> 秒速に変換
$v = (int)(250 * 1000 / 3600);
# 水平方向の速度
$vx = array();
$vx[0] = $v * cos($radian);
# 鉛直方向の速度
$vy = array();
$vy[0] = $v * sin($radian);
# 経過秒数
$t = 0.0;
# 位置
$x = array();
$x[0] = 0.0;
$y = array();
$y[0] = 0.0;

# Runge-Kutta-Gill法
for ($i = 1; $y[0] >= 0.0; $i++)
{
    # 経過秒数
    $t = $i * $h;

    # 位置・速度
    $x[1]  = $h *    $vx[0];
    $y[1]  = $h *    $vy[0];
    $vx[1] = $h * fx($vx[0], $vy[0]);
    $vy[1] = $h * fy($vx[0], $vy[0]);

    $wx = $vx[0] + $vx[1] / 2;
    $wy = $vy[0] + $vy[1] / 2;
    $x[2]  = $h *    $wx;
    $y[2]  = $h *    $wy;
    $vx[2] = $h * fx($wx, $wy);
    $vy[2] = $h * fy($wx, $wy);

    $wx    = $vx[0] + $vx[1] * ((sqrt(2.0) - 1) / 2) + $vx[2] * (1 - 1 / sqrt(2.0));
    $wy    = $vy[0] + $vy[1] * ((sqrt(2.0) - 1) / 2) + $vy[2] * (1 - 1 / sqrt(2.0));
    $x[3]  = $h *    $wx;
    $y[3]  = $h *    $wy;
    $vx[3] = $h * fx($wx, $wy);
    $vy[3] = $h * fy($wx, $wy);

    $wx    = $vx[0] - $vx[2] / sqrt(2.0) + $vx[3] * (1 + 1 / sqrt(2.0));
    $wy    = $vy[0] - $vy[2] / sqrt(2.0) + $vy[3] * (1 + 1 / sqrt(2.0));
    $x[4]  = $h *    $wx;
    $y[4]  = $h *    $wy;
    $vx[4] = $h * fx($wx, $wy);
    $vy[4] = $h * fy($wx, $wy);

    $x[0]  += ( $x[1] +  $x[2] * (2 - sqrt(2.0)) +  $x[3] * (2 + sqrt(2.0)) +  $x[4]) / 6;
    $y[0]  += ( $y[1] +  $y[2] * (2 - sqrt(2.0)) +  $y[3] * (2 + sqrt(2.0)) +  $y[4]) / 6;
    $vx[0] += ($vx[1] + $vx[2] * (2 - sqrt(2.0)) + $vx[3] * (2 + sqrt(2.0)) + $vx[4]) / 6;
    $vy[0] += ($vy[1] + $vy[2] * (2 - sqrt(2.0)) + $vy[3] * (2 + sqrt(2.0)) + $vy[4]) / 6;

    printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", $t, $vx[0], $vy[0], $x[0], $y[0]);
}

# 空気抵抗による水平方向の減速分
function fx($vx, $vy)
{
    global $k;
    return $k * sqrt($vx * $vx + $vy * $vy) * $vx;
}
# 重力と空気抵抗による鉛直方向の減速分
function fy($vx, $vy)
{
    global $g, $k;
    return $g + ($k * sqrt($vx * $vx + $vy * $vy) * $vy);
}
?>

Z:\>php Z:\0805.php
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

Python

# coding: Shift_JIS

import math

# 重力加速度
g = -9.8
# 空気抵抗係数
k = -0.01
# 時間間隔(秒)
h = 0.01

# 角度
degree = 45
radian = degree * math.pi / 180.0
# 初速 250 km/h -> 秒速に変換
v = int(250 * 1000 / 3600)
# 水平方向の速度
vx = [0 for i in range(5)]
vx[0] = v * math.cos(radian)
# 鉛直方向の速度
vy = [0 for i in range(5)]
vy[0] = v * math.sin(radian)
# 経過秒数
t = 0.0
# 位置
x = [0 for i in range(5)]
x[0] = 0.0
y = [0 for i in range(5)]
y[0] = 0.0

# 空気抵抗による水平方向の減速分
def fx(vx, vy):
    return k * math.sqrt(vx * vx + vy * vy) * vx

# 重力と空気抵抗による鉛直方向の減速分
def fy(vx, vy):
    return g + (k * math.sqrt(vx * vx + vy * vy) * vy)

# Runge-Kutta-Gill法
i = 1
while y[0] >= 0.0:
    # 経過秒数
    t = i * h

    # 位置・速度
    x[1]  = h *    vx[0]
    y[1]  = h *    vy[0]
    vx[1] = h * fx(vx[0], vy[0])
    vy[1] = h * fy(vx[0], vy[0])

    wx    = vx[0] + vx[1] / 2
    wy    = vy[0] + vy[1] / 2
    x[2]  = h *    wx
    y[2]  = h *    wy
    vx[2] = h * fx(wx, wy)
    vy[2] = h * fy(wx, wy)

    wx    = vx[0] + vx[1] * ((math.sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / math.sqrt(2.0))
    wy    = vy[0] + vy[1] * ((math.sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / math.sqrt(2.0))
    x[3]  = h *    wx
    y[3]  = h *    wy
    vx[3] = h * fx(wx, wy)
    vy[3] = h * fy(wx, wy)

    wx    = vx[0] - vx[2] / math.sqrt(2.0) + vx[3] * (1 + 1 / math.sqrt(2.0))
    wy    = vy[0] - vy[2] / math.sqrt(2.0) + vy[3] * (1 + 1 / math.sqrt(2.0))
    x[4]  = h *    wx
    y[4]  = h *    wy
    vx[4] = h * fx(wx, wy)
    vy[4] = h * fy(wx, wy)

    x[0]  += ( x[1] +  x[2] * (2 - math.sqrt(2.0)) +  x[3] * (2 + math.sqrt(2.0)) +  x[4]) / 6
    y[0]  += ( y[1] +  y[2] * (2 - math.sqrt(2.0)) +  y[3] * (2 + math.sqrt(2.0)) +  y[4]) / 6
    vx[0] += (vx[1] + vx[2] * (2 - math.sqrt(2.0)) + vx[3] * (2 + math.sqrt(2.0)) + vx[4]) / 6
    vy[0] += (vy[1] + vy[2] * (2 - math.sqrt(2.0)) + vy[3] * (2 + math.sqrt(2.0)) + vy[4]) / 6

    print "%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f" % (t, vx[0], vy[0], x[0], y[0])

    i += 1

Z:\>python Z:\0805.py
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

Ruby

# 重力加速度
$g = -9.8
# 空気抵抗係数
$k = -0.01
# 時間間隔(秒)
h = 0.01

# 角度
degree = 45
radian = degree * Math::PI / 180.0
# 初速 250 km/h -> 秒速に変換
v = 250 * 1000 / 3600
# 水平方向の速度
vx = Array.new(5)
vx[0] = v * Math.cos(radian)
# 鉛直方向の速度
vy = Array.new(5)
vy[0] = v * Math.sin(radian)
# 経過秒数
t = 0.0
# 位置
x = Array.new(5)
x[0] = 0.0
y = Array.new(5)
y[0] = 0.0

# 空気抵抗による水平方向の減速分
def fx(vx, vy)
    return $k * Math.sqrt(vx * vx + vy * vy) * vx
end

# 重力と空気抵抗による鉛直方向の減速分
def fy(vx, vy)
    return $g + ($k * Math.sqrt(vx * vx + vy * vy) * vy)
end

# Runge-Kutta-Gill法
i = 1
while y[0] >= 0.0 do
    # 経過秒数
    t = i * h

    # 位置・速度
    x[1]  = h *    vx[0]
    y[1]  = h *    vy[0]
    vx[1] = h * fx(vx[0], vy[0])
    vy[1] = h * fy(vx[0], vy[0])

    wx    = vx[0] + vx[1] / 2
    wy    = vy[0] + vy[1] / 2
    x[2]  = h *    wx
    y[2]  = h *    wy
    vx[2] = h * fx(wx, wy)
    vy[2] = h * fy(wx, wy)

    wx    = vx[0] + vx[1] * ((Math.sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / Math.sqrt(2.0))
    wy    = vy[0] + vy[1] * ((Math.sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / Math.sqrt(2.0))
    x[3]  = h *    wx
    y[3]  = h *    wy
    vx[3] = h * fx(wx, wy)
    vy[3] = h * fy(wx, wy)

    wx    = vx[0] - vx[2] / Math.sqrt(2.0) + vx[3] * (1 + 1 / Math.sqrt(2.0))
    wy    = vy[0] - vy[2] / Math.sqrt(2.0) + vy[3] * (1 + 1 / Math.sqrt(2.0))
    x[4]  = h *    wx
    y[4]  = h *    wy
    vx[4] = h * fx(wx, wy)
    vy[4] = h * fy(wx, wy)

    x[0]  += ( x[1] +  x[2] * (2 - Math.sqrt(2.0)) +  x[3] * (2 + Math.sqrt(2.0)) +  x[4]) / 6
    y[0]  += ( y[1] +  y[2] * (2 - Math.sqrt(2.0)) +  y[3] * (2 + Math.sqrt(2.0)) +  y[4]) / 6
    vx[0] += (vx[1] + vx[2] * (2 - Math.sqrt(2.0)) + vx[3] * (2 + Math.sqrt(2.0)) + vx[4]) / 6
    vy[0] += (vy[1] + vy[2] * (2 - Math.sqrt(2.0)) + vy[3] * (2 + Math.sqrt(2.0)) + vy[4]) / 6

    printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", t, vx[0], vy[0], x[0], y[0])

    i += 1
end

Z:\>ruby Z:\0805.rb
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

Groovy

Pascal

program Pas0805(arg);
{$MODE delphi}

uses
    SysUtils, Math;

const
    // 重力加速度
    g = -9.8;
    // 空気抵抗係数
    k = -0.01;
    // 時間間隔(秒)
    h = 0.01;
    // 角度
    degree = 45;

// 空気抵抗による水平方向の減速分
function fx(vx:Double; vy:Double):Double;
begin
    result := k * Sqrt(vx * vx + vy * vy) * vx;
end;

// 重力と空気抵抗による鉛直方向の減速分
function fy(vx:Double; vy:Double):Double;
begin
    result := g + (k * Sqrt(vx * vx + vy * vy) * vy);
end;

var
    // 角度
    radian:Double;
    // 初速
    v:Double;
    // 水平方向の速度
    vx:array [0..4] of Double;
    wx:Double;
    // 鉛直方向の速度
    vy:array [0..4] of Double;
    wy:Double;
    // 経過秒数
    t:Double = 0.0;
    // 位置
    x:array [0..4] of Double;
    y:array [0..4] of Double;

    i:Integer;
begin
    // 角度
    radian := degree * PI / 180.0;
    // 初速 250 km/h -> 秒速に変換
    v := 250 * 1000 div 3600;
    // 水平方向の速度
    vx[0] := v * Cos(radian);
    // 鉛直方向の速度
    vy[0] := v * Sin(radian);
    // 位置
    x[0] := 0.0;
    y[0] := 0.0;

    // Runge-Kutta-Gill法
    i := 1;
    while y[0] >= 0.0 do
    begin
        // 経過秒数
        t := i * h;

        // 位置・速度
        x[1]  := h *    vx[0];
        y[1]  := h *    vy[0];
        vx[1] := h * fx(vx[0], vy[0]);
        vy[1] := h * fy(vx[0], vy[0]);

        wx    := vx[0] + vx[1] / 2;
        wy    := vy[0] + vy[1] / 2;
        x[2]  := h *    wx;
        y[2]  := h *    wy;
        vx[2] := h * fx(wx, wy);
        vy[2] := h * fy(wx, wy);

        wx    := vx[0] + vx[1] * ((Sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / Sqrt(2.0));
        wy    := vy[0] + vy[1] * ((Sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / Sqrt(2.0));
        x[3]  := h *    wx;
        y[3]  := h *    wy;
        vx[3] := h * fx(wx, wy);
        vy[3] := h * fy(wx, wy);

        wx    := vx[0] - vx[2] / Sqrt(2.0) + vx[3] * (1 + 1 / Sqrt(2.0));
        wy    := vy[0] - vy[2] / Sqrt(2.0) + vy[3] * (1 + 1 / Sqrt(2.0));
        x[4]  := h *    wx;
        y[4]  := h *    wy;
        vx[4] := h * fx(wx, wy);
        vy[4] := h * fy(wx, wy);

        x[0]  := x[0]  + ( x[1] +  x[2] * (2 - Sqrt(2.0)) +  x[3] * (2 + Sqrt(2.0)) +  x[4]) / 6;
        y[0]  := y[0]  + ( y[1] +  y[2] * (2 - Sqrt(2.0)) +  y[3] * (2 + Sqrt(2.0)) +  y[4]) / 6;
        vx[0] := vx[0] + (vx[1] + vx[2] * (2 - Sqrt(2.0)) + vx[3] * (2 + Sqrt(2.0)) + vx[4]) / 6;
        vy[0] := vy[0] + (vy[1] + vy[2] * (2 - Sqrt(2.0)) + vy[3] * (2 + Sqrt(2.0)) + vy[4]) / 6;

        writeln(format('%4.2f'#9'%8.5f'#9'%9.5f'#9'%9.5f'#9'%9.5f', [t, vx[0], vy[0], x[0], y[0]]));

        inc(i);
    end;
end.

Z:\>fpc -v0 -l- Pas0805.pp

Z:\>Pas0805
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

Ada

with TEXT_IO, Ada.Long_Float_Text_IO, Ada.Numerics, Ada.Numerics.Long_Elementary_Functions;
use  TEXT_IO, Ada.Long_Float_Text_IO, Ada.Numerics, Ada.Numerics.Long_Elementary_Functions;

procedure Ada0805 is
    -- 重力加速度
    g : Constant Long_Float := -9.8;
    -- 空気抵抗係数
    k : Constant Long_Float := -0.01;
    -- 時間間隔(秒)
    h : Constant Long_Float := 0.01;
    -- 角度
    degree : Constant Long_Float := 45.0;

    -- 空気抵抗による水平方向の減速分
    function fx(vx:Long_Float; vy:Long_Float) return Long_Float is
    begin
        return k * Sqrt(vx * vx + vy * vy) * vx;
    end fx;

    -- 重力と空気抵抗による鉛直方向の減速分
    function fy(vx:Long_Float; vy:Long_Float) return Long_Float is
    begin
        return g + (k * Sqrt(vx * vx + vy * vy) * vy);
    end fy;

    -- 角度
    radian:Long_Float;
    -- 初速
    v:Long_Float;
    -- 水平方向の速度
    vx:array (0..4) of Long_Float;
    wx:Long_Float;
    -- 鉛直方向の速度
    vy:array (0..4) of Long_Float;
    wy:Long_Float;
    -- 経過秒数
    t:Long_Float := 0.0;
    -- 位置
    x:array (0..4) of Long_Float;
    y:array (0..4) of Long_Float;

    i:Integer;
begin
    -- 角度
    radian := degree * Pi / 180.0;
    -- 初速 250 km/h -> 秒速に変換
    v := Long_Float(250 * 1000 / 3600);
    -- 水平方向の速度
    vx(0) := v * Cos(radian);
    -- 鉛直方向の速度
    vy(0) := v * Sin(radian);
    -- 位置
    x(0) := 0.0;
    y(0) := 0.0;

    -- Runge-Kutta-Gill法
    i := 1;
    while y(0) >= 0.0 loop
        -- 経過秒数
        t := Long_Float(i) * h;

        -- 位置・速度
        x(1)  := h *    vx(0);
        y(1)  := h *    vy(0);
        vx(1) := h * fx(vx(0), vy(0));
        vy(1) := h * fy(vx(0), vy(0));

        wx    := vx(0) + vx(1) / 2.0;
        wy    := vy(0) + vy(1) / 2.0;
        x(2)  := h *    wx;
        y(2)  := h *    wy;
        vx(2) := h * fx(wx, wy);
        vy(2) := h * fy(wx, wy);

        wx    := vx(0) + vx(1) * ((Sqrt(2.0) - 1.0) / 2.0) + vx(2) * (1.0 - 1.0 / Sqrt(2.0));
        wy    := vy(0) + vy(1) * ((Sqrt(2.0) - 1.0) / 2.0) + vy(2) * (1.0 - 1.0 / Sqrt(2.0));
        x(3)  := h *    wx;
        y(3)  := h *    wy;
        vx(3) := h * fx(wx, wy);
        vy(3) := h * fy(wx, wy);

        wx    := vx(0) - vx(2) / Sqrt(2.0) + vx(3) * (1.0 + 1.0 / Sqrt(2.0));
        wy    := vy(0) - vy(2) / Sqrt(2.0) + vy(3) * (1.0 + 1.0 / Sqrt(2.0));
        x(4)  := h *    wx;
        y(4)  := h *    wy;
        vx(4) := h * fx(wx, wy);
        vy(4) := h * fy(wx, wy);

        x(0)  := x(0)  + ( x(1) +  x(2) * (2.0 - Sqrt(2.0)) +  x(3) * (2.0 + Sqrt(2.0)) +  x(4)) / 6.0;
        y(0)  := y(0)  + ( y(1) +  y(2) * (2.0 - Sqrt(2.0)) +  y(3) * (2.0 + Sqrt(2.0)) +  y(4)) / 6.0;
        vx(0) := vx(0) + (vx(1) + vx(2) * (2.0 - Sqrt(2.0)) + vx(3) * (2.0 + Sqrt(2.0)) + vx(4)) / 6.0;
        vy(0) := vy(0) + (vy(1) + vy(2) * (2.0 - Sqrt(2.0)) + vy(3) * (2.0 + Sqrt(2.0)) + vy(4)) / 6.0;

        Put(t,       Fore=>1, Aft=>2, Exp=>0);
        Put(Ascii.HT);
        Put(vx(0),   Fore=>3, Aft=>5, Exp=>0);
        Put(Ascii.HT);
        Put(vy(0),   Fore=>4, Aft=>5, Exp=>0);
        Put(Ascii.HT);
        Put(x(0),    Fore=>4, Aft=>5, Exp=>0);
        Put(Ascii.HT);
        Put(y(0),    Fore=>4, Aft=>5, Exp=>0);
        New_Line;

        i := i + 1;
    end loop;
end Ada0805;

xxxxxx@yyyyyy /Z
$ gnatmake Ada0805.adb

xxxxxx@yyyyyy /Z
$ Ada0805
0.01     48.45619     48.35852     0.48623     0.48574
0.02     48.12689     47.93222     0.96914     0.96719
0.03     47.80236     47.51133     1.44878     1.44440
0.04     47.48250     47.09575     1.92520     1.91743
0.05     47.16722     46.68537     2.39845     2.38633
0.06     46.85642     46.28007     2.86856     2.85116
0.07     46.55001     45.87974     3.33559     3.31195
0.08     46.24790     45.48430     3.79958     3.76877
0.09     45.94999     45.09363     4.26056     4.22165
省略
6.20      9.25063    -23.74826   125.74997     2.41410
6.21      9.22707    -23.78565   125.84236     2.17643
6.22      9.20355    -23.82289   125.93451     1.93839
6.23      9.18006    -23.85997   126.02643     1.69997
6.24      9.15661    -23.89690   126.11811     1.46119
6.25      9.13319    -23.93366   126.20956     1.22203
6.26      9.10982    -23.97027   126.30078     0.98251
6.27      9.08647    -24.00673   126.39176     0.74263
6.28      9.06317    -24.04303   126.48251     0.50238
6.29      9.03990    -24.07917   126.57302     0.26177
6.30      9.01667    -24.11516   126.66330     0.02080
6.31      8.99347    -24.15100   126.75335    -0.22053

VB.NET

Option Explicit

Module VB0805
    '重力加速度
    Private Const g As Double = -9.8
    '空気抵抗係数
    Private Const k As Double = -0.01
    '時間間隔(秒)
    Private Const h As Double = 0.01

    Public Sub Main()
        '角度
        Const degree As Double = 45
        Dim radian As Double = degree * Math.PI / 180.0
        '初速 250 km/h -> 秒速に変換
        Dim v As Double = 250 * 1000 \ 3600
        '水平方向の速度
        Dim vx(5) As Double
        vx(0) = v * Math.Cos(radian)
        '鉛直方向の速度
        Dim vy(5) As Double
        vy(0) = v * Math.Sin(radian)
        '経過秒数
        Dim t As Double = 0.0
        '位置
        Dim x(5) As Double
        x(0) = 0.0
        Dim y(5) As Double
        y(0) = 0.0

        'Runge-Kutta-Gill法
        Dim i As Integer = 1
        Do While (y(0) >= 0.0)
            '経過秒数
            t = i * h

            '位置・速度
            x(1)  = h *    vx(0)
            y(1)  = h *    vy(0)
            vx(1) = h * fx(vx(0), vy(0))
            vy(1) = h * fy(vx(0), vy(0))

            Dim wx As Double = vx(0) + vx(1) / 2.0
            Dim wy As Double = vy(0) + vy(1) / 2.0
            x(2)  = h *    wx
            y(2)  = h *    wy
            vx(2) = h * fx(wx, wy)
            vy(2) = h * fy(wx, wy)

            wx    = vx(0) + vx(1) * ((Math.Sqrt(2.0) - 1) / 2) + vx(2) * (1 - 1 / Math.Sqrt(2.0))
            wy    = vy(0) + vy(1) * ((Math.Sqrt(2.0) - 1) / 2) + vy(2) * (1 - 1 / Math.Sqrt(2.0))
            x(3)  = h *    wx
            y(3)  = h *    wy
            vx(3) = h * fx(wx, wy)
            vy(3) = h * fy(wx, wy)

            wx    = vx(0) - vx(2) / Math.Sqrt(2.0) + vx(3) * (1 + 1 / Math.Sqrt(2.0))
            wy    = vy(0) - vy(2) / Math.Sqrt(2.0) + vy(3) * (1 + 1 / Math.Sqrt(2.0))
            x(4)  = h *    wx
            y(4)  = h *    wy
            vx(4) = h * fx(wx, wy)
            vy(4) = h * fy(wx, wy)

            x(0)  += ( x(1) +  x(2) * (2 - Math.Sqrt(2.0)) +  x(3) * (2 + Math.Sqrt(2.0)) +  x(4)) / 6
            y(0)  += ( y(1) +  y(2) * (2 - Math.Sqrt(2.0)) +  y(3) * (2 + Math.Sqrt(2.0)) +  y(4)) / 6
            vx(0) += (vx(1) + vx(2) * (2 - Math.Sqrt(2.0)) + vx(3) * (2 + Math.Sqrt(2.0)) + vx(4)) / 6
            vy(0) += (vy(1) + vy(2) * (2 - Math.Sqrt(2.0)) + vy(3) * (2 + Math.Sqrt(2.0)) + vy(4)) / 6

            Console.WriteLine(String.Format("{0,4:F2}{5}{1,8:F5}{5}{2,9:F5}{5}{3,9:F5}{5}{4,9:F5}", t, vx(0), vy(0), x(0), y(0), vbTab))

            i += 1
        Loop
    End Sub

    '空気抵抗による水平方向の減速分
    Private Function fx(ByVal vx As Double, ByVal vy As Double) As Double
        Return k * Math.Sqrt(vx * vx + vy * vy) * vx
    End Function

    '重力と空気抵抗による鉛直方向の減速分
    Private Function fy(ByVal vx As Double, ByVal vy As Double) As Double
        Return g + (k * Math.Sqrt(vx * vx + vy * vy) * vy)
    End Function
End Module

Z:\>vbc -nologo VB0805.vb

Z:\>VB0805
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

C#

using System;

public class CS0805
{
    // 重力加速度
    private const double g = -9.8;
    // 空気抵抗係数
    private const double k = -0.01;
    // 時間間隔(秒)
    private const double h = 0.01;

    public static void Main()
    {
        // 角度
        double degree = 45;
        double radian = degree * Math.PI / 180.0;
        // 初速 250 km/h -> 秒速に変換
        double v = 250 * 1000 / 3600;
        // 水平方向の速度
        double[] vx = new double[5];
        vx[0] = v * Math.Cos(radian);
        // 鉛直方向の速度
        double[] vy = new double[5];
        vy[0] = v * Math.Sin(radian);
        // 経過秒数
        double t = 0.0;
        // 位置
        double[] x = new double[5];
        x[0] = 0.0;
        double[] y = new double[5];
        y[0] = 0.0;

        // Runge-Kutta-Gill法
        for (int i = 1; y[0] >= 0.0; i++)
        {
            // 経過秒数
            t = i * h;

            // 位置・速度
            x[1]  = h *    vx[0];
            y[1]  = h *    vy[0];
            vx[1] = h * fx(vx[0], vy[0]);
            vy[1] = h * fy(vx[0], vy[0]);

            double wx = vx[0] + vx[1] / 2;
            double wy = vy[0] + vy[1] / 2;
            x[2]  = h *    wx;
            y[2]  = h *    wy;
            vx[2] = h * fx(wx, wy);
            vy[2] = h * fy(wx, wy);

            wx    = vx[0] + vx[1] * ((Math.Sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / Math.Sqrt(2.0));
            wy    = vy[0] + vy[1] * ((Math.Sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / Math.Sqrt(2.0));
            x[3]  = h *    wx;
            y[3]  = h *    wy;
            vx[3] = h * fx(wx, wy);
            vy[3] = h * fy(wx, wy);

            wx    = vx[0] - vx[2] / Math.Sqrt(2.0) + vx[3] * (1 + 1 / Math.Sqrt(2.0));
            wy    = vy[0] - vy[2] / Math.Sqrt(2.0) + vy[3] * (1 + 1 / Math.Sqrt(2.0));
            x[4]  = h *    wx;
            y[4]  = h *    wy;
            vx[4] = h * fx(wx, wy);
            vy[4] = h * fy(wx, wy);

            x[0]  += ( x[1] +  x[2] * (2 - Math.Sqrt(2.0)) +  x[3] * (2 + Math.Sqrt(2.0)) +  x[4]) / 6;
            y[0]  += ( y[1] +  y[2] * (2 - Math.Sqrt(2.0)) +  y[3] * (2 + Math.Sqrt(2.0)) +  y[4]) / 6;
            vx[0] += (vx[1] + vx[2] * (2 - Math.Sqrt(2.0)) + vx[3] * (2 + Math.Sqrt(2.0)) + vx[4]) / 6;
            vy[0] += (vy[1] + vy[2] * (2 - Math.Sqrt(2.0)) + vy[3] * (2 + Math.Sqrt(2.0)) + vy[4]) / 6;

            Console.WriteLine(string.Format("{0,4:F2}\t{1,8:F5}\t{2,9:F5}\t{3,9:F5}\t{4,8:F5}", t, vx[0], vy[0], x[0], y[0]));
        }
    }

    // 空気抵抗による水平方向の減速分
    private static double fx(double vx, double vy)
    {
        return k * Math.Sqrt(vx * vx + vy * vy) * vx;
    }
    // 重力と空気抵抗による鉛直方向の減速分
    private static double fy(double vx, double vy)
    {
        return g + (k * Math.Sqrt(vx * vx + vy * vy) * vy);
    }
}

Z:\>csc -nologo CS0805.cs

Z:\>CS0805
0.01    48.45619     48.35852     0.48623    0.48574
0.02    48.12689     47.93222     0.96914    0.96719
0.03    47.80236     47.51133     1.44878    1.44440
0.04    47.48250     47.09575     1.92520    1.91743
0.05    47.16722     46.68537     2.39845    2.38633
0.06    46.85642     46.28007     2.86856    2.85116
0.07    46.55001     45.87974     3.33559    3.31195
0.08    46.24790     45.48430     3.79958    3.76877
0.09    45.94999     45.09363     4.26056    4.22165
省略
6.20     9.25063    -23.74826   125.74997    2.41410
6.21     9.22707    -23.78565   125.84236    2.17643
6.22     9.20355    -23.82289   125.93451    1.93839
6.23     9.18006    -23.85997   126.02643    1.69997
6.24     9.15661    -23.89690   126.11811    1.46119
6.25     9.13319    -23.93366   126.20956    1.22203
6.26     9.10982    -23.97027   126.30078    0.98251
6.27     9.08647    -24.00673   126.39176    0.74263
6.28     9.06317    -24.04303   126.48251    0.50238
6.29     9.03990    -24.07917   126.57302    0.26177
6.30     9.01667    -24.11516   126.66330    0.02080
6.31     8.99347    -24.15100   126.75335   -0.22053

Java

import static java.lang.System.out;

public class Java0805 {

    // 重力加速度
    private static final double g = -9.8;
    // 空気抵抗係数
    private static final double k = -0.01;
    // 時間間隔(秒)
    private static final double h = 0.01;

    public static void main(String []args) {
        // 角度
        double degree = 45;
        double radian = degree * Math.PI / 180.0;
        // 初速 250 km/h -> 秒速に変換
        double v = 250 * 1000 / 3600;
        // 水平方向の速度
        double[] vx = new double[5];
        vx[0] = v * Math.cos(radian);
        // 鉛直方向の速度
        double[] vy = new double[5];
        vy[0] = v * Math.sin(radian);
        // 経過秒数
        double t = 0.0;
        // 位置
        double[] x = new double[5];
        x[0] = 0.0;
        double[] y = new double[5];
        y[0] = 0.0;

        // Runge-Kutta-Gill法
        for (int i = 1; y[0] >= 0.0; i++) {
            // 経過秒数
            t = i * h;

            // 位置・速度
            x[1]  = h *    vx[0];
            y[1]  = h *    vy[0];
            vx[1] = h * fx(vx[0], vy[0]);
            vy[1] = h * fy(vx[0], vy[0]);

            double wx = vx[0] + vx[1] / 2;
            double wy = vy[0] + vy[1] / 2;
            x[2]  = h *    wx;
            y[2]  = h *    wy;
            vx[2] = h * fx(wx, wy);
            vy[2] = h * fy(wx, wy);

            wx    = vx[0] + vx[1] * ((Math.sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / Math.sqrt(2.0));
            wy    = vy[0] + vy[1] * ((Math.sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / Math.sqrt(2.0));
            x[3]  = h *    wx;
            y[3]  = h *    wy;
            vx[3] = h * fx(wx, wy);
            vy[3] = h * fy(wx, wy);

            wx    = vx[0] - vx[2] / Math.sqrt(2.0) + vx[3] * (1 + 1 / Math.sqrt(2.0));
            wy    = vy[0] - vy[2] / Math.sqrt(2.0) + vy[3] * (1 + 1 / Math.sqrt(2.0));
            x[4]  = h *    wx;
            y[4]  = h *    wy;
            vx[4] = h * fx(wx, wy);
            vy[4] = h * fy(wx, wy);

            x[0]  += ( x[1] +  x[2] * (2 - Math.sqrt(2.0)) +  x[3] * (2 + Math.sqrt(2.0)) +  x[4]) / 6;
            y[0]  += ( y[1] +  y[2] * (2 - Math.sqrt(2.0)) +  y[3] * (2 + Math.sqrt(2.0)) +  y[4]) / 6;
            vx[0] += (vx[1] + vx[2] * (2 - Math.sqrt(2.0)) + vx[3] * (2 + Math.sqrt(2.0)) + vx[4]) / 6;
            vy[0] += (vy[1] + vy[2] * (2 - Math.sqrt(2.0)) + vy[3] * (2 + Math.sqrt(2.0)) + vy[4]) / 6;

            out.println(String.format("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f", t, vx[0], vy[0], x[0], y[0]));
        }
    }

    // 空気抵抗による水平方向の減速分
    private static double fx(double vx, double vy) {
        return k * Math.sqrt(vx * vx + vy * vy) * vx;
    }
    // 重力と空気抵抗による鉛直方向の減速分
    private static double fy(double vx, double vy) {
        return g + (k * Math.sqrt(vx * vx + vy * vy) * vy);
    }
}

Z:\>javac Java0805.java

Z:\>java Java0805
0.01    48.45619     48.35852     0.48623    0.48574
0.02    48.12689     47.93222     0.96914    0.96719
0.03    47.80236     47.51133     1.44878    1.44440
0.04    47.48250     47.09575     1.92520    1.91743
0.05    47.16722     46.68537     2.39845    2.38633
0.06    46.85642     46.28007     2.86856    2.85116
0.07    46.55001     45.87974     3.33559    3.31195
0.08    46.24790     45.48430     3.79958    3.76877
0.09    45.94999     45.09363     4.26056    4.22165
省略
6.20     9.25063    -23.74826   125.74997    2.41410
6.21     9.22707    -23.78565   125.84236    2.17643
6.22     9.20355    -23.82289   125.93451    1.93839
6.23     9.18006    -23.85997   126.02643    1.69997
6.24     9.15661    -23.89690   126.11811    1.46119
6.25     9.13319    -23.93366   126.20956    1.22203
6.26     9.10982    -23.97027   126.30078    0.98251
6.27     9.08647    -24.00673   126.39176    0.74263
6.28     9.06317    -24.04303   126.48251    0.50238
6.29     9.03990    -24.07917   126.57302    0.26177
6.30     9.01667    -24.11516   126.66330    0.02080
6.31     8.99347    -24.15100   126.75335   -0.22053

C++

#include <iostream>
#include <iomanip>
#include <math.h>
using namespace std;

// 重力加速度
const double g = -9.8;
// 空気抵抗係数
const double k = -0.01;
// 時間間隔(秒)
const double h = 0.01;

// 空気抵抗による水平方向の減速分
double fx(double vx, double vy);
// 重力と空気抵抗による鉛直方向の減速分
double fy(double vx, double vy);

int main()
{
    // 角度
    double degree = 45;
    double radian = degree * M_PI / 180.0;
    // 初速 250 km/h -> 秒速に変換
    double v = 250 * 1000 / 3600;
    // 水平方向の速度
    double vx[5];
    vx[0] = v * cos(radian);
    // 鉛直方向の速度
    double vy[5];
    vy[0] = v * sin(radian);
    // 経過秒数
    double t = 0.0;
    // 位置
    double x[5];
    x[0] = 0.0;
    double y[5];
    y[0] = 0.0;

    // Runge-Kutta-Gill法
    for (int i = 1; y[0] >= 0.0; i++)
    {
        // 経過秒数
        t = i * h;
        cout << setw(4) << fixed << setprecision(2) << t << "\t";

        // 速度
        x[1]  = h *    vx[0];
        y[1]  = h *    vy[0];
        vx[1] = h * fx(vx[0], vy[0]);
        vy[1] = h * fy(vx[0], vy[0]);

        double wx = vx[0] + vx[1] / 2;
        double wy = vy[0] + vy[1] / 2;
        x[2]  = h *    wx;
        y[2]  = h *    wy;
        vx[2] = h * fx(wx, wy);
        vy[2] = h * fy(wx, wy);

        wx    = vx[0] + vx[1] * ((sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / sqrt(2.0));
        wy    = vy[0] + vy[1] * ((sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / sqrt(2.0));
        x[3]  = h *    wx;
        y[3]  = h *    wy;
        vx[3] = h * fx(wx, wy);
        vy[3] = h * fy(wx, wy);

        wx    = vx[0] - vx[2] / sqrt(2.0) + vx[3] * (1 + 1 / sqrt(2.0));
        wy    = vy[0] - vy[2] / sqrt(2.0) + vy[3] * (1 + 1 / sqrt(2.0));
        x[4]  = h *    wx;
        y[4]  = h *    wy;
        vx[4] = h * fx(wx, wy);
        vy[4] = h * fy(wx, wy);

        x[0]  += ( x[1] +  x[2] * (2 - sqrt(2.0)) +  x[3] * (2 + sqrt(2.0)) +  x[4]) / 6;
        y[0]  += ( y[1] +  y[2] * (2 - sqrt(2.0)) +  y[3] * (2 + sqrt(2.0)) +  y[4]) / 6;
        vx[0] += (vx[1] + vx[2] * (2 - sqrt(2.0)) + vx[3] * (2 + sqrt(2.0)) + vx[4]) / 6;
        vy[0] += (vy[1] + vy[2] * (2 - sqrt(2.0)) + vy[3] * (2 + sqrt(2.0)) + vy[4]) / 6;

        cout << setw(8) << fixed << setprecision(5) << vx[0] << "\t";
        cout << setw(9) << fixed << setprecision(5) << vy[0] << "\t";
        cout << setw(9) << fixed << setprecision(5) <<  x[0] << "\t";
        cout << setw(8) << fixed << setprecision(5) <<  y[0] << endl;
    }
    return 0;
}

// 空気抵抗による水平方向の減速分
double fx(double vx, double vy)
{
    return k * sqrt(vx * vx + vy * vy) * vx;
}
// 重力と空気抵抗による鉛直方向の減速分
double fy(double vx, double vy)
{
    return g + (k * sqrt(vx * vx + vy * vy) * vy);
}

Z:\>bcc32 -q CP0805.cpp
cp0805.cpp:

Z:\>CP0805
0.01    48.45619     48.35852     0.48623    0.48574
0.02    48.12689     47.93222     0.96914    0.96719
0.03    47.80236     47.51133     1.44878    1.44440
0.04    47.48250     47.09575     1.92520    1.91743
0.05    47.16722     46.68537     2.39845    2.38633
0.06    46.85642     46.28007     2.86856    2.85116
0.07    46.55001     45.87974     3.33559    3.31195
0.08    46.24790     45.48430     3.79958    3.76877
0.09    45.94999     45.09363     4.26056    4.22165
省略
6.20     9.25063    -23.74826   125.74997    2.41410
6.21     9.22707    -23.78565   125.84236    2.17643
6.22     9.20355    -23.82289   125.93451    1.93839
6.23     9.18006    -23.85997   126.02643    1.69997
6.24     9.15661    -23.89690   126.11811    1.46119
6.25     9.13319    -23.93366   126.20956    1.22203
6.26     9.10982    -23.97027   126.30078    0.98251
6.27     9.08647    -24.00673   126.39176    0.74263
6.28     9.06317    -24.04303   126.48251    0.50238
6.29     9.03990    -24.07917   126.57302    0.26177
6.30     9.01667    -24.11516   126.66330    0.02080
6.31     8.99347    -24.15100   126.75335   -0.22053

Objective-C

#import <Foundation/Foundation.h>
#import <math.h>

// 重力加速度
const double g = -9.8;
// 空気抵抗係数
const double k = -0.01;
// 時間間隔(秒)
const double h = 0.01;

// 空気抵抗による水平方向の減速分
double fx(double vx, double vy);
// 重力と空気抵抗による鉛直方向の減速分
double fy(double vx, double vy);

int main()
{
    // 角度
    double degree = 45;
    double radian = degree * M_PI / 180.0;
    // 初速 250 km/h -> 秒速に変換
    double v = 250 * 1000 / 3600;
    // 水平方向の速度
    double vx[5];
    vx[0] = v * cos(radian);
    // 鉛直方向の速度
    double vy[5];
    vy[0] = v * sin(radian);
    // 経過秒数
    double t = 0.0;
    // 位置
    double x[5];
    x[0] = 0.0;
    double y[5];
    y[0] = 0.0;

    // Runge-Kutta-Gill法
    int i;
    for (i = 1; y[0] >= 0.0; i++)
    {
        // 経過秒数
        t = i * h;

        // 速度
        x[1]  = h *    vx[0];
        y[1]  = h *    vy[0];
        vx[1] = h * fx(vx[0], vy[0]);
        vy[1] = h * fy(vx[0], vy[0]);

        double wx = vx[0] + vx[1] / 2;
        double wy = vy[0] + vy[1] / 2;
        x[2]  = h *    wx;
        y[2]  = h *    wy;
        vx[2] = h * fx(wx, wy);
        vy[2] = h * fy(wx, wy);

        wx    = vx[0] + vx[1] * ((sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / sqrt(2.0));
        wy    = vy[0] + vy[1] * ((sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / sqrt(2.0));
        x[3]  = h *    wx;
        y[3]  = h *    wy;
        vx[3] = h * fx(wx, wy);
        vy[3] = h * fy(wx, wy);

        wx    = vx[0] - vx[2] / sqrt(2.0) + vx[3] * (1 + 1 / sqrt(2.0));
        wy    = vy[0] - vy[2] / sqrt(2.0) + vy[3] * (1 + 1 / sqrt(2.0));
        x[4]  = h *    wx;
        y[4]  = h *    wy;
        vx[4] = h * fx(wx, wy);
        vy[4] = h * fy(wx, wy);

        x[0]  += ( x[1] +  x[2] * (2 - sqrt(2.0)) +  x[3] * (2 + sqrt(2.0)) +  x[4]) / 6;
        y[0]  += ( y[1] +  y[2] * (2 - sqrt(2.0)) +  y[3] * (2 + sqrt(2.0)) +  y[4]) / 6;
        vx[0] += (vx[1] + vx[2] * (2 - sqrt(2.0)) + vx[3] * (2 + sqrt(2.0)) + vx[4]) / 6;
        vy[0] += (vy[1] + vy[2] * (2 - sqrt(2.0)) + vy[3] * (2 + sqrt(2.0)) + vy[4]) / 6;

        printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", t, vx[0], vy[0], x[0], y[0]);
    }
    return 0;
}

// 空気抵抗による水平方向の減速分
double fx(double vx, double vy)
{
    return k * sqrt(vx * vx + vy * vy) * vx;
}
// 重力と空気抵抗による鉛直方向の減速分
double fy(double vx, double vy)
{
    return g + (k * sqrt(vx * vx + vy * vy) * vy);
}

xxxxxx@yyyyyy /Z
$ gcc -o OC0805 OC0805.m -lobjc -lgnustep-base -I $INCLUDE -L $LIB $CFLAGS

xxxxxx@yyyyyy /Z
$ OC0805
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

D

import std.stdio;
import std.math;

// 重力加速度
const double g = -9.8;
// 空気抵抗係数
const double k = -0.01;
// 時間間隔(秒)
const double h = 0.01;

void main(string[] args)
{
    // 角度
    double degree = 45;
    double radian = degree * PI / 180.0;
    // 初速 250 km/h -> 秒速に変換
    double v = 250 * 1000 / 3600;
    // 水平方向の速度
    double vx[5];
    vx[0] = v * cos(radian);
    // 鉛直方向の速度
    double vy[5];
    vy[0] = v * sin(radian);
    // 経過秒数
    double t = 0.0;
    // 位置
    double x[5];
    x[0] = 0.0;
    double y[5];
    y[0] = 0.0;

    // Runge-Kutta-Gill法
    for (int i = 1; y[0] >= 0.0; i++)
    {
        // 経過秒数
        t = i * h;

        // 速度
        x[1]  = h *    vx[0];
        y[1]  = h *    vy[0];
        vx[1] = h * fx(vx[0], vy[0]);
        vy[1] = h * fy(vx[0], vy[0]);

        double wx = vx[0] + vx[1] / 2;
        double wy = vy[0] + vy[1] / 2;
        x[2]  = h *    wx;
        y[2]  = h *    wy;
        vx[2] = h * fx(wx, wy);
        vy[2] = h * fy(wx, wy);

        wx    = vx[0] + vx[1] * ((sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / sqrt(2.0));
        wy    = vy[0] + vy[1] * ((sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / sqrt(2.0));
        x[3]  = h *    wx;
        y[3]  = h *    wy;
        vx[3] = h * fx(wx, wy);
        vy[3] = h * fy(wx, wy);

        wx    = vx[0] - vx[2] / sqrt(2.0) + vx[3] * (1 + 1 / sqrt(2.0));
        wy    = vy[0] - vy[2] / sqrt(2.0) + vy[3] * (1 + 1 / sqrt(2.0));
        x[4]  = h *    wx;
        y[4]  = h *    wy;
        vx[4] = h * fx(wx, wy);
        vy[4] = h * fy(wx, wy);

        x[0]  += ( x[1] +  x[2] * (2 - sqrt(2.0)) +  x[3] * (2 + sqrt(2.0)) +  x[4]) / 6;
        y[0]  += ( y[1] +  y[2] * (2 - sqrt(2.0)) +  y[3] * (2 + sqrt(2.0)) +  y[4]) / 6;
        vx[0] += (vx[1] + vx[2] * (2 - sqrt(2.0)) + vx[3] * (2 + sqrt(2.0)) + vx[4]) / 6;
        vy[0] += (vy[1] + vy[2] * (2 - sqrt(2.0)) + vy[3] * (2 + sqrt(2.0)) + vy[4]) / 6;

        writefln("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f", t, vx[0], vy[0], x[0], y[0]);
    }
}

// 空気抵抗による水平方向の減速分
double fx(double vx, double vy)
{
    return k * sqrt(vx * vx + vy * vy) * vx;
}
// 重力と空気抵抗による鉛直方向の減速分
double fy(double vx, double vy)
{
    return g + (k * sqrt(vx * vx + vy * vy) * vy);
}

Z:\>dmd D0805.d

Z:\>D0805
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02079
6.31     8.99347    -24.15100   126.75335    -0.22053

Go

package main

import "fmt"
import "math"

// 重力加速度
const g float64 = -9.8
// 空気抵抗係数
const k float64 = -0.01
// 時間間隔(秒)
const h float64 = 0.01

func main() {
    // 角度
    var degree float64 = 45
    var radian float64 = degree * math.Pi / 180.0
    // 初速 250 km/h -> 秒速に変換
    var v float64 = 250 * 1000 / 3600
    // 水平方向の速度
    var vx[5] float64
    vx[0] = v * math.Cos(radian)
    // 鉛直方向の速度
    var vy[5] float64
    vy[0] = v * math.Sin(radian)
    // 経過秒数
    var t float64 = 0.0
    // 位置
    var x[5] float64
    x[0] = 0.0
    var y[5] float64
    y[0] = 0.0

    // Runge-Kutta-Gill法
    for i := 1; y[0] >= 0.0; i++ {
        // 経過秒数
        t = float64(i) * h

        // 位置・速度
        x[1]  = h *    vx[0]
        y[1]  = h *    vy[0]
        vx[1] = h * fx(vx[0], vy[0])
        vy[1] = h * fy(vx[0], vy[0])

        var wx float64 = vx[0] + vx[1] / 2
        var wy float64 = vy[0] + vy[1] / 2
        x[2]  = h *    wx
        y[2]  = h *    wy
        vx[2] = h * fx(wx, wy)
        vy[2] = h * fy(wx, wy)

        wx    = vx[0] + vx[1] * ((math.Sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / math.Sqrt(2.0))
        wy    = vy[0] + vy[1] * ((math.Sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / math.Sqrt(2.0))
        x[3]  = h *    wx
        y[3]  = h *    wy
        vx[3] = h * fx(wx, wy)
        vy[3] = h * fy(wx, wy)

        wx    = vx[0] - vx[2] / math.Sqrt(2.0) + vx[3] * (1 + 1 / math.Sqrt(2.0))
        wy    = vy[0] - vy[2] / math.Sqrt(2.0) + vy[3] * (1 + 1 / math.Sqrt(2.0))
        x[4]  = h *    wx
        y[4]  = h *    wy
        vx[4] = h * fx(wx, wy)
        vy[4] = h * fy(wx, wy)

        x[0]  += ( x[1] +  x[2] * (2 - math.Sqrt(2.0)) +  x[3] * (2 + math.Sqrt(2.0)) +  x[4]) / 6
        y[0]  += ( y[1] +  y[2] * (2 - math.Sqrt(2.0)) +  y[3] * (2 + math.Sqrt(2.0)) +  y[4]) / 6
        vx[0] += (vx[1] + vx[2] * (2 - math.Sqrt(2.0)) + vx[3] * (2 + math.Sqrt(2.0)) + vx[4]) / 6
        vy[0] += (vy[1] + vy[2] * (2 - math.Sqrt(2.0)) + vy[3] * (2 + math.Sqrt(2.0)) + vy[4]) / 6

        fmt.Printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", t, vx[0], vy[0], x[0], y[0])
    }
}

// 空気抵抗による水平方向の減速分
func fx(vx float64, vy float64) float64 {
    return k * math.Sqrt(vx * vx + vy * vy) * vx
}
// 重力と空気抵抗による鉛直方向の減速分
func fy(vx float64, vy float64) float64 {
    return g + (k * math.Sqrt(vx * vx + vy * vy) * vy)
}

Z:\>8g GO0805.go

Z:\>8l -o GO0805.exe GO0805.8

Z:\>GO0805
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

Scala

object Scala0804 {

    // 重力加速度
    val g = -9.8
    // 空気抵抗係数
    val k = -0.01
    // 時間間隔(秒)
    val h = 0.01

    def main(args: Array[String]) {
        // 角度
        val degree = 45
        val radian = degree * Math.PI / 180.0
        // 初速 250 km/h -> 秒速に変換
        val v = 250 * 1000 / 3600
        // 水平方向の速度
        val vx = v * Math.cos(radian)
        // 鉛直方向の速度
        val vy = v * Math.sin(radian)
        // 位置
        val x = 0.0
        val y = 0.0

        // Runge-Kutta-Gill法
        rungekuttagill(1, vx, vy, x, y)
    }

    def rungekuttagill(i:Int, vx:Double, vy:Double, x:Double, y:Double):Unit = {
        // 経過秒数
        val t = i * h

        // 位置・速度
        val wx1  = h *    vx
        val wy1  = h *    vy
        val wvx1 = h * fx(vx, vy)
        val wvy1 = h * fy(vx, vy)

        val wvx5 = vx + wvx1 / 2
        val wvy5 = vy + wvy1 / 2
        val wx2  = h *    wvx5
        val wy2  = h *    wvy5
        val wvx2 = h * fx(wvx5, wvy5)
        val wvy2 = h * fy(wvx5, wvy5)

        val wvx6 = vx + wvx1 * ((Math.sqrt(2.0) - 1) / 2) + wvx2 * (1 - 1 / Math.sqrt(2.0))
        val wvy6 = vy + wvy1 * ((Math.sqrt(2.0) - 1) / 2) + wvy2 * (1 - 1 / Math.sqrt(2.0))
        val wx3  = h *    wvx6
        val wy3  = h *    wvy6
        val wvx3 = h * fx(wvx6, wvy6)
        val wvy3 = h * fy(wvx6, wvy6)

        val wvx7 = vx - wvx2 / Math.sqrt(2.0) + wvx3 * (1 + 1 / Math.sqrt(2.0))
        val wvy7 = vy - wvy2 / Math.sqrt(2.0) + wvy3 * (1 + 1 / Math.sqrt(2.0))
        val wx4  = h *    wvx7
        val wy4  = h *    wvy7
        val wvx4 = h * fx(wvx7, wvy7)
        val wvy4 = h * fy(wvx7, wvy7)

        val wx  = x  + ( wx1 +  wx2 * (2 - Math.sqrt(2.0)) +  wx3 * (2 + Math.sqrt(2.0)) +  wx4) / 6
        val wy  = y  + ( wy1 +  wy2 * (2 - Math.sqrt(2.0)) +  wy3 * (2 + Math.sqrt(2.0)) +  wy4) / 6
        val wvx = vx + (wvx1 + wvx2 * (2 - Math.sqrt(2.0)) + wvx3 * (2 + Math.sqrt(2.0)) + wvx4) / 6
        val wvy = vy + (wvy1 + wvy2 * (2 - Math.sqrt(2.0)) + wvy3 * (2 + Math.sqrt(2.0)) + wvy4) / 6

        println("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f".format(t, wvx, wvy, wx, wy))

        if (wy >= 0.0)
            rungekuttagill(i+1, wvx, wvy, wx, wy)
        else
            ()
    }

    // 空気抵抗による水平方向の減速分
    def fx(vx:Double, vy:Double) = {
        k * Math.sqrt(vx * vx + vy * vy) * vx
    }
    // 重力と空気抵抗による鉛直方向の減速分
    def fy(vx:Double, vy:Double) = {
        g + (k * Math.sqrt(vx * vx + vy * vy) * vy)
    }
}

Z:\>scala Scala0805.scala
0.01    48.45619     48.35852     0.48623    0.48574
0.02    48.12689     47.93222     0.96914    0.96719
0.03    47.80236     47.51133     1.44878    1.44440
0.04    47.48250     47.09575     1.92520    1.91743
0.05    47.16722     46.68537     2.39845    2.38633
0.06    46.85642     46.28007     2.86856    2.85116
0.07    46.55001     45.87974     3.33559    3.31195
0.08    46.24790     45.48430     3.79958    3.76877
0.09    45.94999     45.09363     4.26056    4.22165
省略
6.20     9.25063    -23.74826   125.74997    2.41410
6.21     9.22707    -23.78565   125.84236    2.17643
6.22     9.20355    -23.82289   125.93451    1.93839
6.23     9.18006    -23.85997   126.02643    1.69997
6.24     9.15661    -23.89690   126.11811    1.46119
6.25     9.13319    -23.93366   126.20956    1.22203
6.26     9.10982    -23.97027   126.30078    0.98251
6.27     9.08647    -24.00673   126.39176    0.74263
6.28     9.06317    -24.04303   126.48251    0.50238
6.29     9.03990    -24.07917   126.57302    0.26177
6.30     9.01667    -24.11516   126.66330    0.02080
6.31     8.99347    -24.15100   126.75335   -0.22053

F#

module Fs0805

open System

// 重力加速度
let g = -9.8
// 空気抵抗係数
let k = -0.01
// 時間間隔(秒)
let h = 0.01

// 角度
let degree = 45.0
let radian = degree * Math.PI / 180.0
// 初速 250 km/h -> 秒速に変換
let v = float(250 * 1000 / 3600)
// 水平方向の速度
let vx = v * Math.Cos(radian)
// 鉛直方向の速度
let vy = v * Math.Sin(radian)
// 位置
let x = 0.0
let y = 0.0

// 空気抵抗による水平方向の減速分
let fx(vx:Double) (vy:Double) =
    k * Math.Sqrt(vx * vx + vy * vy) * vx
// 重力と空気抵抗による鉛直方向の減速分
let fy(vx:Double) (vy:Double) =
    g + (k * Math.Sqrt(vx * vx + vy * vy) * vy)

// Runge-Kutta-Gill法
let rec rungekuttagill(i:int) (vx:double) (vy:double) (x:double) (y:double):unit =
    // 経過秒数
    let t = float(i) * h

    // 位置・速度
    let wx1  = h *     vx
    let wy1  = h *     vy
    let wvx1 = h * (fx vx vy)
    let wvy1 = h * (fy vx vy)

    let wvx5 = vx + wvx1 / 2.0
    let wvy5 = vy + wvy1 / 2.0
    let wx2  = h *     wvx5
    let wy2  = h *     wvy5
    let wvx2 = h * (fx wvx5 wvy5)
    let wvy2 = h * (fy wvx5 wvy5)

    let wvx6 = vx + wvx1 * ((Math.Sqrt(2.0) - 1.0) / 2.0) + wvx2 * (1.0 - 1.0 / Math.Sqrt(2.0))
    let wvy6 = vy + wvy1 * ((Math.Sqrt(2.0) - 1.0) / 2.0) + wvy2 * (1.0 - 1.0 / Math.Sqrt(2.0))
    let wx3  = h *     wvx6
    let wy3  = h *     wvy6
    let wvx3 = h * (fx wvx6 wvy6)
    let wvy3 = h * (fy wvx6 wvy6)

    let wvx7 = vx - wvx2 / Math.Sqrt(2.0) + wvx3 * (1.0 + 1.0 / Math.Sqrt(2.0))
    let wvy7 = vy - wvy2 / Math.Sqrt(2.0) + wvy3 * (1.0 + 1.0 / Math.Sqrt(2.0))
    let wx4  = h *     wvx7
    let wy4  = h *     wvy7
    let wvx4 = h * (fx wvx7 wvy7)
    let wvy4 = h * (fy wvx7 wvy7)

    let wx  = x  + ( wx1 +  wx2 * (2.0 - Math.Sqrt(2.0)) +  wx3 * (2.0 + Math.Sqrt(2.0)) +  wx4) / 6.0
    let wy  = y  + ( wy1 +  wy2 * (2.0 - Math.Sqrt(2.0)) +  wy3 * (2.0 + Math.Sqrt(2.0)) +  wy4) / 6.0
    let wvx = vx + (wvx1 + wvx2 * (2.0 - Math.Sqrt(2.0)) + wvx3 * (2.0 + Math.Sqrt(2.0)) + wvx4) / 6.0
    let wvy = vy + (wvy1 + wvy2 * (2.0 - Math.Sqrt(2.0)) + wvy3 * (2.0 + Math.Sqrt(2.0)) + wvy4) / 6.0

    printfn "%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f" t wvx wvy wx wy

    if wy >= 0.0 then
        (rungekuttagill (i+1) wvx wvy wx wy)
    else
        ()

// Runge-Kutta-Gill法
(rungekuttagill 1 vx vy x y)

exit 0

Z:\>fsi  --nologo --quiet Fs0805.fs
0.01    48.45619     48.35852     0.48623    0.48574
0.02    48.12689     47.93222     0.96914    0.96719
0.03    47.80236     47.51133     1.44878    1.44440
0.04    47.48250     47.09575     1.92520    1.91743
0.05    47.16722     46.68537     2.39845    2.38633
0.06    46.85642     46.28007     2.86856    2.85116
0.07    46.55001     45.87974     3.33559    3.31195
0.08    46.24790     45.48430     3.79958    3.76877
0.09    45.94999     45.09363     4.26056    4.22165
省略
6.20     9.25063    -23.74826   125.74997    2.41410
6.21     9.22707    -23.78565   125.84236    2.17643
6.22     9.20355    -23.82289   125.93451    1.93839
6.23     9.18006    -23.85997   126.02643    1.69997
6.24     9.15661    -23.89690   126.11811    1.46119
6.25     9.13319    -23.93366   126.20956    1.22203
6.26     9.10982    -23.97027   126.30078    0.98251
6.27     9.08647    -24.00673   126.39176    0.74263
6.28     9.06317    -24.04303   126.48251    0.50238
6.29     9.03990    -24.07917   126.57302    0.26177
6.30     9.01667    -24.11516   126.66330    0.02080
6.31     8.99347    -24.15100   126.75335   -0.22053

Clojure

; 重力加速度
(def g -9.8)
; 空気抵抗係数
(def k -0.01)
; 時間間隔(秒)
(def h 0.01)

; 角度
(def degree 45.0)
(def radian (* degree (/ (. Math PI) 180.0)))
; 初速 250 km/h -> 秒速に変換
(def v (quot (* 250 1000) 3600))
; 水平方向の速度
(def vx (* v (. Math cos radian)))
; 鉛直方向の速度
(def vy (* v (. Math sin radian)))
; 位置
(def x 0.0)
(def y 0.0)

; 空気抵抗による水平方向の減速分
(defn fx[vx vy]
    (* k (* (. Math sqrt (+ (* vx vx) (* vy vy))) vx)))
; 重力と空気抵抗による鉛直方向の減速分
(defn fy[vx vy]
    (+ g (* k (* (. Math sqrt (+ (* vx vx) (* vy vy))) vy))))

; Runge-Kutta-Gill法
(defn rungekuttagill[i vx vy x y]
    ; 経過秒数
    (def t (* i h))

    ; 位置・速度
    (def wx1  (* h     vx))
    (def wy1  (* h     vy))
    (def wvx1 (* h (fx vx vy)))
    (def wvy1 (* h (fy vx vy)))

    (def wvx5 (+ vx (/ wvx1 2.0)))
    (def wvy5 (+ vy (/ wvy1 2.0)))
    (def wx2  (* h     wvx5))
    (def wy2  (* h     wvy5))
    (def wvx2 (* h (fx wvx5 wvy5)))
    (def wvy2 (* h (fy wvx5 wvy5)))

    (def wvx6 (+ vx (* wvx1 (/ (- (. Math sqrt 2.0) 1.0) 2.0)) (* wvx2 (- 1.0 (/ 1.0 (. Math sqrt 2.0))))))
    (def wvy6 (+ vy (* wvy1 (/ (- (. Math sqrt 2.0) 1.0) 2.0)) (* wvy2 (- 1.0 (/ 1.0 (. Math sqrt 2.0))))))
    (def wx3  (* h     wvx6))
    (def wy3  (* h     wvy6))
    (def wvx3 (* h (fx wvx6 wvy6)))
    (def wvy3 (* h (fy wvx6 wvy6)))

    (def wvx7 (+ (- vx (/ wvx2 (. Math sqrt 2.0))) (* wvx3 (+ 1.0 (/ 1.0 (. Math sqrt 2.0))))))
    (def wvy7 (+ (- vy (/ wvy2 (. Math sqrt 2.0))) (* wvy3 (+ 1.0 (/ 1.0 (. Math sqrt 2.0))))))
    (def wx4  (* h     wvx7))
    (def wy4  (* h     wvy7))
    (def wvx4 (* h (fx wvx7 wvy7)))
    (def wvy4 (* h (fy wvx7 wvy7)))

    (def wx  (+ x  (/ (+  wx1 (*  wx2 (- 2.0 (. Math sqrt 2.0))) (*  wx3 (+ 2.0 (. Math sqrt 2.0)))  wx4) 6.0)))
    (def wy  (+ y  (/ (+  wy1 (*  wy2 (- 2.0 (. Math sqrt 2.0))) (*  wy3 (+ 2.0 (. Math sqrt 2.0)))  wy4) 6.0)))
    (def wvx (+ vx (/ (+ wvx1 (* wvx2 (- 2.0 (. Math sqrt 2.0))) (* wvx3 (+ 2.0 (. Math sqrt 2.0))) wvx4) 6.0)))
    (def wvy (+ vy (/ (+ wvy1 (* wvy2 (- 2.0 (. Math sqrt 2.0))) (* wvy3 (+ 2.0 (. Math sqrt 2.0))) wvy4) 6.0)))

    (println (format "%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f" t wvx wvy wx wy))

    (if (>= wy 0.0)
        (rungekuttagill (+ i 1) wvx wvy wx wy)
        nil))

(rungekuttagill 1 vx vy x y)

Z:\>java -cp C:\ProgramFiles\clojure-1.5.1\clojure-1.5.1.jar clojure.main Clj0805.clj
0.01    48.45619     48.35852     0.48623     0.48574
0.02    48.12689     47.93222     0.96914     0.96719
0.03    47.80236     47.51133     1.44878     1.44440
0.04    47.48250     47.09575     1.92520     1.91743
0.05    47.16722     46.68537     2.39845     2.38633
0.06    46.85642     46.28007     2.86856     2.85116
0.07    46.55001     45.87974     3.33559     3.31195
0.08    46.24790     45.48430     3.79958     3.76877
0.09    45.94999     45.09363     4.26056     4.22165
省略
6.20     9.25063    -23.74826   125.74997     2.41410
6.21     9.22707    -23.78565   125.84236     2.17643
6.22     9.20355    -23.82289   125.93451     1.93839
6.23     9.18006    -23.85997   126.02643     1.69997
6.24     9.15661    -23.89690   126.11811     1.46119
6.25     9.13319    -23.93366   126.20956     1.22203
6.26     9.10982    -23.97027   126.30078     0.98251
6.27     9.08647    -24.00673   126.39176     0.74263
6.28     9.06317    -24.04303   126.48251     0.50238
6.29     9.03990    -24.07917   126.57302     0.26177
6.30     9.01667    -24.11516   126.66330     0.02080
6.31     8.99347    -24.15100   126.75335    -0.22053

Haskell

import Text.Printf

-- 重力加速度
g = -9.8 :: Double
-- 空気抵抗係数
k = -0.01 :: Double
-- 時間間隔(秒)
h = 0.01 :: Double

-- 空気抵抗による水平方向の減速分
fx::Double->Double->Double
fx vx vy =
    let
        v = sqrt(vx * vx + vy * vy)
    in
        k * v * vx

-- 空気抵抗による鉛直方向の減速分
fy::Double->Double->Double
fy vx vy =
    let
        v = sqrt(vx * vx + vy * vy)
    in
        g + (k * v * vy)

-- Runge-Kutta-Gill法
rungekuttagill::Integer->Double->Double->Double->Double->IO ()
rungekuttagill i vx vy x y =
    let
        -- 経過秒数
        t = (fromIntegral i) * h

        -- 位置・速度
        wx1  = h *     vx
        wy1  = h *     vy
        wvx1 = h * (fx vx vy)
        wvy1 = h * (fy vx vy)

        wvx5 = vx + wvx1 / 2.0
        wvy5 = vy + wvy1 / 2.0
        wx2  = h *     wvx5
        wy2  = h *     wvy5
        wvx2 = h * (fx wvx5 wvy5)
        wvy2 = h * (fy wvx5 wvy5)

        wvx6 = vx + wvx1 * ((sqrt(2.0) - 1.0) / 2.0) + wvx2 * (1.0 - 1.0 / sqrt(2.0))
        wvy6 = vy + wvy1 * ((sqrt(2.0) - 1.0) / 2.0) + wvy2 * (1.0 - 1.0 / sqrt(2.0))
        wx3  = h *     wvx6
        wy3  = h *     wvy6
        wvx3 = h * (fx wvx6 wvy6)
        wvy3 = h * (fy wvx6 wvy6)

        wvx7 = vx - wvx2 / sqrt(2.0) + wvx3 * (1.0 + 1.0 / sqrt(2.0))
        wvy7 = vy - wvy2 / sqrt(2.0) + wvy3 * (1.0 + 1.0 / sqrt(2.0))
        wx4  = h *     wvx7
        wy4  = h *     wvy7
        wvx4 = h * (fx wvx7 wvy7)
        wvy4 = h * (fy wvx7 wvy7)

        wx  = x  + ( wx1 +  wx2 * (2.0 - sqrt(2.0)) +  wx3 * (2.0 + sqrt(2.0)) +  wx4) / 6.0
        wy  = y  + ( wy1 +  wy2 * (2.0 - sqrt(2.0)) +  wy3 * (2.0 + sqrt(2.0)) +  wy4) / 6.0
        wvx = vx + (wvx1 + wvx2 * (2.0 - sqrt(2.0)) + wvx3 * (2.0 + sqrt(2.0)) + wvx4) / 6.0
        wvy = vy + (wvy1 + wvy2 * (2.0 - sqrt(2.0)) + wvy3 * (2.0 + sqrt(2.0)) + wvy4) / 6.0
    in
        if y >= 0.0
            then do
                printf "%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f\n" t wvx wvy wx wy
                rungekuttagill (i+1) wvx wvy wx wy
            else
                return ()

main = do
    -- 角度
    let degree = 45.0 :: Double
    let radian = degree * pi / 180.0
    -- 初速 250 km/h -> 秒速に変換
    let v = (fromIntegral (250 * 1000 `div` 3600))

    -- 水平方向の速度
    let vx = v * cos(radian)
    -- 鉛直方向の速度
    let vy = v * sin(radian)
    -- 位置
    let x = 0.0
    let y = 0.0

    -- Runge-Kutta-Gill法
    rungekuttagill 1 vx vy x y

Z:\>runghc Hs0805.hs
0.01    48.45619     48.35852     0.48623    0.48574
0.02    48.12689     47.93222     0.96914    0.96719
0.03    47.80236     47.51133     1.44878    1.44440
0.04    47.48250     47.09575     1.92520    1.91743
0.05    47.16722     46.68537     2.39845    2.38633
0.06    46.85642     46.28007     2.86856    2.85116
0.07    46.55001     45.87974     3.33559    3.31195
0.08    46.24790     45.48430     3.79958    3.76877
0.09    45.94999     45.09363     4.26056    4.22165
省略
6.20     9.25063    -23.74826   125.74997    2.41410
6.21     9.22707    -23.78565   125.84236    2.17643
6.22     9.20355    -23.82289   125.93451    1.93839
6.23     9.18006    -23.85997   126.02643    1.69997
6.24     9.15661    -23.89690   126.11811    1.46119
6.25     9.13319    -23.93366   126.20956    1.22203
6.26     9.10982    -23.97027   126.30078    0.98251
6.27     9.08647    -24.00673   126.39176    0.74263
6.28     9.06317    -24.04303   126.48251    0.50238
6.29     9.03990    -24.07917   126.57302    0.26177
6.30     9.01667    -24.11516   126.66330    0.02080
6.31     8.99347    -24.15100   126.75335   -0.22053