さまざまな言語で数値計算

中点法

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, 中点法で計算する
(空気抵抗係数を 0.01 で計算)

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(1)
vx(0) = v * Cos(radian)
'鉛直方向の速度
Private vy(): ReDim vy(1)
vy(0) = v * Sin(radian)
'経過秒数
Private t: t = 0.0
'位置
Private x(): ReDim x(1)
x(0) = 0.0
Private y(): ReDim y(1)
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

'中点法
Dim i: i = 1
Do While (y(0) >= 0.0)
    '経過秒数
    t = i * h

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

    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(8) & FormatNumber(y(0),  5, -1, 0, 0), 8)

    i = i + 1
Loop

Z:\>cscript //nologo Z:\0803.vbs
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994

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

// 中点法
for (var i = 1; y[0] >= 0.0; i++)
{
    // 経過秒数
    t = i * h

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

    var wx = vx[0] + vx[1] / 2.0
    var wy = vy[0] + vy[1] / 2.0
    vx[0]  = vx[0] + h * fx(wx, wy)
    vy[0]  = vy[0] + h * fy(wx, wy)
    x[0]   = x[0]  + h *    wx
    y[0]   = y[0]  + h *    wy

    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:\0803.js
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994

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[] 2
$vx[0] = $v * [Math]::Cos($radian)
# 鉛直方向の速度
$vy  = New-Object double[] 2
$vy[0] = $v * [Math]::Sin($radian)
# 経過秒数
$t = 0.0
# 位置
$x  = New-Object double[] 2
$y  = New-Object double[] 2
$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)
}

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

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

    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:\0803.ps1
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994

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;

# 中点法
for (my $i = 1; $y[0] >= 0.0; $i++)
{
    # 経過秒数
    $t = $i * $h;

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

    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:\0803.pl
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

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;

# 中点法
for ($i = 1; $y[0] >= 0.0; $i++)
{
    # 経過秒数
    $t = $i * $h;

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

    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:\0803.php
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

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(3)]
vx[0] = v * math.cos(radian)
# 鉛直方向の速度
vy = [0 for i in range(3)]
vy[0] = v * math.sin(radian)
# 経過秒数
t = 0.0
# 位置
x = [0 for i in range(3)]
x[0] = 0.0
y = [0 for i in range(3)]
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)

# 中点法
i = 1
while y[0] >= 0.0:
    # 経過秒数
    t = i * h

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

    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:\0803.py
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

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(2)
vx[0] = v * Math.cos(radian)
# 鉛直方向の速度
vy = Array.new(2)
vy[0] = v * Math.sin(radian)
# 経過秒数
t = 0.0
# 位置
x = Array.new(2)
x[0] = 0.0
y = Array.new(2)
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

# 中点法
i = 1
while y[0] >= 0.0 do
    # 経過秒数
    t = i * h

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

    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:\0803.rb
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

Groovy

Pascal

program Pas0803(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..1] of Double;
    wx:Double;
    // 鉛直方向の速度
    vy:array [0..1] of Double;
    wy:Double;
    // 経過秒数
    t:Double = 0.0;
    // 位置
    x:array [0..1] of Double;
    y:array [0..1] 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;

    // 中点法
    i := 1;
    while y[0] >= 0.0 do
    begin
        // 経過秒数
        t := i * h;

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

        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- Pas0803.pp

Z:\>Pas0803
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

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 Ada0803 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..1) of Long_Float;
    wx:Long_Float;
    -- 鉛直方向の速度
    vy:array (0..1) of Long_Float;
    wy:Long_Float;
    -- 経過秒数
    t:Long_Float := 0.0;
    -- 位置
    x:array (0..1) of Long_Float;
    y:array (0..1) 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;

    -- 中点法
    i := 1;
    while y(0) >= 0.0 loop
        -- 経過秒数
        t := Long_Float(i) * h;

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

        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 Ada0803;

xxxxxx@yyyyyy /Z
$ gnatmake Ada0803.adb

xxxxxx@yyyyyy /Z
$ Ada0803
0.01     48.45620     48.35854     0.48622     0.48573
0.02     48.12691     47.93225     0.96912     0.96717
0.03     47.80240     47.51138     1.44876     1.44438
0.04     47.48255     47.09581     1.92517     1.91740
0.05     47.16729     46.68543     2.39841     2.38629
0.06     46.85650     46.28014     2.86852     2.85111
0.07     46.55009     45.87983     3.33554     3.31189
0.08     46.24799     45.48440     3.79952     3.76870
0.09     45.95010     45.09374     4.26050     4.22158
省略
6.20      9.25071    -23.74815   125.75040     2.41468
6.21      9.22715    -23.78555   125.84279     2.17702
6.22      9.20362    -23.82279   125.93494     1.93897
6.23      9.18014    -23.85987   126.02686     1.70056
6.24      9.15669    -23.89679   126.11854     1.46178
6.25      9.13327    -23.93356   126.20999     1.22262
6.26      9.10989    -23.97017   126.30121     0.98311
6.27      9.08655    -24.00663   126.39219     0.74322
6.28      9.06325    -24.04293   126.48294     0.50297
6.29      9.03998    -24.07907   126.57346     0.26236
6.30      9.01674    -24.11506   126.66374     0.02139
6.31      8.99355    -24.15090   126.75379    -0.21994

VB.NET

Option Explicit

Module VB0803
    '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(1) As Double
        vx(0) = v * Math.Cos(radian)
        '鉛直方向の速度
        Dim vy(1) As Double
        vy(0) = v * Math.Sin(radian)
        '経過秒数
        Dim t As Double = 0.0
        '位置
        Dim x(1) As Double
        x(0) = 0.0
        Dim y(1) As Double
        y(0) = 0.0

        '中点法
        Dim i As Integer = 1
        Do While (y(0) >= 0.0)
            '経過秒数
            t = i * h

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

            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 VB0803.vb

Z:\>VB0803
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

C#

using System;

public class CS0803
{
    // 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[2];
        vx[0] = v * Math.Cos(radian);
        // 鉛直方向の速度
        double[] vy = new double[2];
        vy[0] = v * Math.Sin(radian);
        // 経過秒数
        double t = 0.0;
        // 位置
        double[] x = new double[2];
        x[0] = 0.0;
        double[] y = new double[2];
        y[0] = 0.0;

        // 中点法
        for (int i = 1; y[0] >= 0.0; i++)
        {
            // 経過秒数
            t = i * h;

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

            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 CS0803.cs

Z:\>CS0803
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994

Java

import static java.lang.System.out;

public class Java0803 {

    // 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[2];
        vx[0] = v * Math.cos(radian);
        // 鉛直方向の速度
        double[] vy = new double[2];
        vy[0] = v * Math.sin(radian);
        // 経過秒数
        double t = 0.0;
        // 位置
        double[] x = new double[2];
        x[0] = 0.0;
        double[] y = new double[2];
        y[0] = 0.0;

        // 中点法
        for (int i = 1; y[0] >= 0.0; i++) {
            // 経過秒数
            t = i * h;

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

            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 Java0803.java

Z:\>java Java0803
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994

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[2];
    vx[0] = v * cos(radian);
    // 鉛直方向の速度
    double vy[2];
    vy[0] = v * sin(radian);
    // 経過秒数
    double t = 0.0;
    // 位置
    double x[2];
    x[0] = 0.0;
    double y[2];
    y[0] = 0.0;

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

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

        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 CP0803.cpp
cp0803.cpp:

Z:\>CP0803
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994

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[2];
    vx[0] = v * cos(radian);
    // 鉛直方向の速度
    double vy[2];
    vy[0] = v * sin(radian);
    // 経過秒数
    double t = 0.0;
    // 位置
    double x[2];
    x[0] = 0.0;
    double y[2];
    y[0] = 0.0;

    // 中点法
    int i;
    for (i = 1; y[0] >= 0.0; i++)
    {
        // 経過秒数
        t = i * h;

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

        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 OC0803 OC0803.m -lobjc -lgnustep-base -I $INCLUDE -L $LIB $CFLAGS

xxxxxx@yyyyyy /Z
$ OC0803
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

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[2];
    vx[0] = v * cos(radian);
    // 鉛直方向の速度
    double vy[2];
    vy[0] = v * sin(radian);
    // 経過秒数
    double t = 0.0;
    // 位置
    double x[2];
    x[0] = 0.0;
    double y[2];
    y[0] = 0.0;

    // 中点法
    for (int i = 1; y[0] >= 0.0; i++)
    {
        // 経過秒数
        t = i * h;

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

        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 D0803.d

Z:\>D0803
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

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[2] float64
    vx[0] = v * math.Cos(radian)
    // 鉛直方向の速度
    var vy[2] float64
    vy[0] = v * math.Sin(radian)
    // 経過秒数
    var t float64 = 0.0
    // 位置
    var x[2] float64
    x[0] = 0.0
    var y[2] float64
    y[0] = 0.0

    // 中点法
    for i := 1; y[0] >= 0.0; i++ {
        // 経過秒数
        t = float64(i) * h

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

        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 GO0803.go

Z:\>8l -o GO0803.exe GO0803.8

Z:\>GO0803
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

Scala

object Scala0803 {

    // 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

        // 中点法
        midpoint(1, vx, vy, x, y)
    }

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

        // 位置・速度
        val wvx1 = h * fx(vx, vy)
        val wvy1 = h * fy(vx, vy)
        val wvx2 = vx + wvx1 / 2
        val wvy2 = vy + wvy1 / 2

        val wvx = vx + h * fx(wvx2, wvy2)
        val wvy = vy + h * fy(wvx2, wvy2)
        val wx  = x  + h *    wvx2
        val wy  = y  + h *    wvy2

        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)
            midpoint(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 Scala0803.scala
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994

F#

module Fs0803

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)

// 中点法
let rec midpoint(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 wvx1 = h * (fx vx vy)
    let wvy1 = h * (fy vx vy)
    let wvx2 = vx + wvx1 / 2.0
    let wvy2 = vy + wvy1 / 2.0

    let wvx = vx + h * (fx wvx2 wvy2)
    let wvy = vy + h * (fy wvx2 wvy2)
    let wx  = x  + h *     wvx2
    let wy  = y  + h *     wvy2

    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
        (midpoint (i+1) wvx wvy wx wy)
    else
        ()

// 中点法
(midpoint 1 vx vy x y)

exit 0

Z:\>fsi  --nologo --quiet Fs0803.fs
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994

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))))

;中点法
(defn midpoint[i vx vy x y]
    ; 経過秒数
    (def t (* i h))

    ; 位置・速度
    (def wvx1 (* h (fx vx vy)))
    (def wvy1 (* h (fy vx vy)))
    (def wvx2 (+ vx (/ wvx1 2.0)))
    (def wvy2 (+ vy (/ wvy1 2.0)))

    (def wvx  (+ vx (* h (fx wvx2 wvy2))))
    (def wvy  (+ vy (* h (fy wvx2 wvy2))))
    (def wx   (+ x  (* h     wvx2)))
    (def wy   (+ y  (* h     wvy2)))

    (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)
        (midpoint (+ i 1) wvx wvy wx wy)
        nil))

(midpoint 1 vx vy x y)

Z:\>java -cp C:\ProgramFiles\clojure-1.5.1\clojure-1.5.1.jar clojure.main Clj0803.clj
0.01    48.45620     48.35854     0.48622     0.48573
0.02    48.12691     47.93225     0.96912     0.96717
0.03    47.80240     47.51138     1.44876     1.44438
0.04    47.48255     47.09581     1.92517     1.91740
0.05    47.16729     46.68543     2.39841     2.38629
0.06    46.85650     46.28014     2.86852     2.85111
0.07    46.55009     45.87983     3.33554     3.31189
0.08    46.24799     45.48440     3.79952     3.76870
0.09    45.95010     45.09374     4.26050     4.22158
省略
6.20     9.25071    -23.74815   125.75040     2.41468
6.21     9.22715    -23.78555   125.84279     2.17702
6.22     9.20362    -23.82279   125.93494     1.93897
6.23     9.18014    -23.85987   126.02686     1.70056
6.24     9.15669    -23.89679   126.11854     1.46178
6.25     9.13327    -23.93356   126.20999     1.22262
6.26     9.10989    -23.97017   126.30121     0.98311
6.27     9.08655    -24.00663   126.39219     0.74322
6.28     9.06325    -24.04293   126.48294     0.50297
6.29     9.03998    -24.07907   126.57346     0.26236
6.30     9.01674    -24.11506   126.66374     0.02139
6.31     8.99355    -24.15090   126.75379    -0.21994

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)

-- 中点法
midpoint::Integer->Double->Double->Double->Double->IO ()
midpoint i vx vy x y =
    let
        -- 経過秒数
        t = (fromIntegral i) * h

        -- 位置・速度
        wvx1 = h * (fx vx vy)
        wvy1 = h * (fy vx vy)
        wvx2 = vx + wvx1 / 2.0
        wvy2 = vy + wvy1 / 2.0

        wvx = vx + h * (fx wvx2 wvy2)
        wvy = vy + h * (fy wvx2 wvy2)
        wx  = x  + h *     wvx2
        wy  = y  + h *     wvy2
    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
                midpoint (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

    -- 中点法
    midpoint 1 vx vy x y

Z:\>runghc Hs0803.hs
0.01    48.45620     48.35854     0.48622    0.48573
0.02    48.12691     47.93225     0.96912    0.96717
0.03    47.80240     47.51138     1.44876    1.44438
0.04    47.48255     47.09581     1.92517    1.91740
0.05    47.16729     46.68543     2.39841    2.38629
0.06    46.85650     46.28014     2.86852    2.85111
0.07    46.55009     45.87983     3.33554    3.31189
0.08    46.24799     45.48440     3.79952    3.76870
0.09    45.95010     45.09374     4.26050    4.22158
省略
6.20     9.25071    -23.74815   125.75040    2.41468
6.21     9.22715    -23.78555   125.84279    2.17702
6.22     9.20362    -23.82279   125.93494    1.93897
6.23     9.18014    -23.85987   126.02686    1.70056
6.24     9.15669    -23.89679   126.11854    1.46178
6.25     9.13327    -23.93356   126.20999    1.22262
6.26     9.10989    -23.97017   126.30121    0.98311
6.27     9.08655    -24.00663   126.39219    0.74322
6.28     9.06325    -24.04293   126.48294    0.50297
6.29     9.03998    -24.07907   126.57346    0.26236
6.30     9.01674    -24.11506   126.66374    0.02139
6.31     8.99355    -24.15090   126.75379   -0.21994