本文介绍了计算球的弹跳的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！
问题描述
我基本上只是想让一个球从比如说100倍反弹到300倍……我寻找抛物型方程，然后寻找三角函数，但我似乎无法让它正常工作。我已经有一段时间没有做数学了，所以我可能甚至没有正确地接近这一点。这是我的整个弹跳代码，如果有人能给我指出正确的方程式，那就太好了。 private void btStart_Click(object sender, EventArgs e)
{
lbBall.Location = new Point(0, 0);
bounceBall(lbBall, 100);
}
public void bounceBall(Label ball, int xFinal)
{
//this just initiales variables and timers
this.animateTimer = new Timer();
this.animateTimer.Interval = 75;
this.animateTimer.Tick += animateTimer_Tick;
this.ball = ball;
this.xInit = ball.Location.X;
this.yInit = ball.Location.Y;
this.xCurrent = ball.Location.X;
this.yCurrent = ball.Location.Y;
this.xFinal = ball.Location.X + xFinal;
this.maxHeight = 100;
this.animateTimer.Start();
}
private void animateTimer_Tick(object sender, EventArgs e)
{
//this just makes sure the timer stops and doesn't go on forever
if (xCurrent >= xFinal)
{
ball.Location = new Point((int)xFinal, (int)yInit);
animateTimer.Stop();
return;
}
//adds 1 to x on every iteration
xCurrent = xCurrent + 1;
//calculates yCurrent based on xCurrent
double result = 0;
float dx = (xCurrent - xInit) / (xFinal - xInit);
if (dx < 0.5)
{
double dxA = Math.Asin(dx);
result = (Math.Sin(dxA)) * maxHeight;
}
else
{
dx = (float)0.5 - dx;
double dxA = Math.Acos(dx);
result = (Math.Cos(dxA)) * maxHeight;
}
yCurrent = (float)result;
ball.Location = new Point((int)xCurrent, (int)yCurrent);
lbLocation.Text = "xPos: " + xCurrent + " yPos: " + yCurrent;
}
推荐答案
无法完全确定您在此处使用三角函数的原因，适用的公式是用于恒定加速系统的suvat公式。
基本上，你在水平轴上没有加速度，所以你的位置(位移)是时间的恒定倍数。
但是，在垂直轴上，重力起了作用，因此您需要根据(A)：
来计算位移 1 2
s = ut + - at
2
其中：
s是要计算的位移；u为初始速度；t为已用时间；a为加速度(g=9.8 m/s/s)。
t的水平位置将为(假设您的投掷方向为正)：
t hpos
--- ----
0.0 0
0.1 1
0.2 2
0.3 3
垂直位置稍微复杂一些。初始垂直速度是零，因为你水平地抛出它，所以我们可以打折ut项。但另一项取决于加速度，因为我们认为加速度是正数，可以理解为-9.8。
因此，从20米高的线开始的垂直位移为：
t vpos
--- --------
0.0 0.000
0.1 -0.049
0.2 -0.196
0.3 -0.441
:
2.0 -19.600
2.1 -21.609
现在请注意，在时间t = 2.0和t = 2.1之间的某个时间，球已通过低于地面，因此您将需要实现具有某种能量损失系数的反弹功能(球在反弹中将损失能量，因此这不仅仅是速度反转的问题，相反，它将类似于能量损失10%的v <- -.9 * v)。
(A)你必须处理反弹的事实意味着你需要知道每个时间点的当前位移和速度是多少，这样你才能处理它。上面给出的s公式假定没有任何东西会妨碍您的对象。
因此，您需要存储对象的位置和当前速度，并使用类似s = s + (v * td) + (0.5 * a * td * td)的内容来更新位置，在必要时处理反弹(通过反转速度和损失能量)，然后v = v + (a * td)更新速度(其中td是与前一状态的时间差)。
举个例子，这是一个相当简单的C程序，它使用这些公式来弹跳一个球，直到它停止(这里没有水平运动，因为它是一个简单的加法方程，所以不是必须的)：
#include <stdio.h>
static void outData (double h, double v, int t) {
printf ("Time t = %4d.%d, veloc = %5.2f, height = %5.2f
",
t / 10, t % 10, v, h);
}
int main(void) {
double td = 0.1, h = 20, a = -9.8 * td, v = 0, lasth = h;
int tenthT = 0;
outData (h, v, 0);
while ((h != 0) || (lasth != 0)) {
lasth = h;
if (h == 0)
v = -0.9 * v;
v = v + a;
h = h + (v * td) + (a * td * td / 2);
if (h < 0)
h = 0;
outData (h, v, tenthT++);
}
return 0;
}
这显示了基于给定公式的球的高度，初始高度为20米，时间增量为十分之一秒。
查看输出(特别是高度)以查看其运行情况：
Time t = 0.0, veloc = 0.00, height = 20.00
Time t = 0.0, veloc = -0.98, height = 19.90
Time t = 0.1, veloc = -1.96, height = 19.70
Time t = 0.2, veloc = -2.94, height = 19.40
Time t = 0.3, veloc = -3.92, height = 19.00
Time t = 0.4, veloc = -4.90, height = 18.51
Time t = 0.5, veloc = -5.88, height = 17.91
Time t = 0.6, veloc = -6.86, height = 17.22
Time t = 0.7, veloc = -7.84, height = 16.43
Time t = 0.8, veloc = -8.82, height = 15.55
Time t = 0.9, veloc = -9.80, height = 14.56
Time t = 1.0, veloc = -10.78, height = 13.48
Time t = 1.1, veloc = -11.76, height = 12.30
Time t = 1.2, veloc = -12.74, height = 11.02
Time t = 1.3, veloc = -13.72, height = 9.64
Time t = 1.4, veloc = -14.70, height = 8.17
Time t = 1.5, veloc = -15.68, height = 6.59
Time t = 1.6, veloc = -16.66, height = 4.92
Time t = 1.7, veloc = -17.64, height = 3.15
Time t = 1.8, veloc = -18.62, height = 1.29
Time t = 1.9, veloc = -19.60, height = 0.00
Time t = 2.0, veloc = 16.66, height = 1.66
Time t = 2.1, veloc = 15.68, height = 3.22
Time t = 2.2, veloc = 14.70, height = 4.69
Time t = 2.3, veloc = 13.72, height = 6.06
Time t = 2.4, veloc = 12.74, height = 7.33
Time t = 2.5, veloc = 11.76, height = 8.50
Time t = 2.6, veloc = 10.78, height = 9.57
Time t = 2.7, veloc = 9.80, height = 10.54
Time t = 2.8, veloc = 8.82, height = 11.42
Time t = 2.9, veloc = 7.84, height = 12.20
Time t = 3.0, veloc = 6.86, height = 12.88
Time t = 3.1, veloc = 5.88, height = 13.47
Time t = 3.2, veloc = 4.90, height = 13.95
Time t = 3.3, veloc = 3.92, height = 14.34
Time t = 3.4, veloc = 2.94, height = 14.63
Time t = 3.5, veloc = 1.96, height = 14.82
Time t = 3.6, veloc = 0.98, height = 14.91
Time t = 3.7, veloc = -0.00, height = 14.91
Time t = 3.8, veloc = -0.98, height = 14.80
Time t = 3.9, veloc = -1.96, height = 14.60
Time t = 4.0, veloc = -2.94, height = 14.30
Time t = 4.1, veloc = -3.92, height = 13.91
Time t = 4.2, veloc = -4.90, height = 13.41
Time t = 4.3, veloc = -5.88, height = 12.82
Time t = 4.4, veloc = -6.86, height = 12.13
Time t = 4.5, veloc = -7.84, height = 11.34
Time t = 4.6, veloc = -8.82, height = 10.45
Time t = 4.7, veloc = -9.80, height = 9.47
Time t = 4.8, veloc = -10.78, height = 8.38
Time t = 4.9, veloc = -11.76, height = 7.20
Time t = 5.0, veloc = -12.74, height = 5.92
Time t = 5.1, veloc = -13.72, height = 4.55
Time t = 5.2, veloc = -14.70, height = 3.07
Time t = 5.3, veloc = -15.68, height = 1.50
Time t = 5.4, veloc = -16.66, height = 0.00
Time t = 5.5, veloc = 14.01, height = 1.40
Time t = 5.6, veloc = 13.03, height = 2.70
Time t = 5.7, veloc = 12.05, height = 3.90
Time t = 5.8, veloc = 11.07, height = 5.00
Time t = 5.9, veloc = 10.09, height = 6.00
Time t = 6.0, veloc = 9.11, height = 6.91
Time t = 6.1, veloc = 8.13, height = 7.72
Time t = 6.2, veloc = 7.15, height = 8.43
Time t = 6.3, veloc = 6.17, height = 9.04
Time t = 6.4, veloc = 5.19, height = 9.56
Time t = 6.5, veloc = 4.21, height = 9.97
Time t = 6.6, veloc = 3.23, height = 10.29
Time t = 6.7, veloc = 2.25, height = 10.51
Time t = 6.8, veloc = 1.27, height = 10.63
Time t = 6.9, veloc = 0.29, height = 10.66
Time t = 7.0, veloc = -0.69, height = 10.58
Time t = 7.1, veloc = -1.67, height = 10.41
Time t = 7.2, veloc = -2.65, height = 10.14
Time t = 7.3, veloc = -3.63, height = 9.78
Time t = 7.4, veloc = -4.61, height = 9.31
Time t = 7.5, veloc = -5.59, height = 8.75
Time t = 7.6, veloc = -6.57, height = 8.09
Time t = 7.7, veloc = -7.55, height = 7.33
Time t = 7.8, veloc = -8.53, height = 6.47
Time t = 7.9, veloc = -9.51, height = 5.51
Time t = 8.0, veloc = -10.49, height = 4.46
Time t = 8.1, veloc = -11.47, height = 3.31
Time t = 8.2, veloc = -12.45, height = 2.06
Time t = 8.3, veloc = -13.43, height = 0.71
Time t = 8.4, veloc = -14.41, height = 0.00
Time t = 8.5, veloc = 11.99, height = 1.19
Time t = 8.6, veloc = 11.01, height = 2.29
Time t = 8.7, veloc = 10.03, height = 3.29
Time t = 8.8, veloc = 9.05, height = 4.19
Time t = 8.9, veloc = 8.07, height = 4.99
Time t = 9.0, veloc = 7.09, height = 5.69
Time t = 9.1, veloc = 6.11, height = 6.30
Time t = 9.2, veloc = 5.13, height = 6.81
Time t = 9.3, veloc = 4.15, height = 7.21
Time t = 9.4, veloc = 3.17, height = 7.53
Time t = 9.5, veloc = 2.19, height = 7.74
Time t = 9.6, veloc = 1.21, height = 7.86
Time t = 9.7, veloc = 0.23, height = 7.87
Time t = 9.8, veloc = -0.75, height = 7.79
Time t = 9.9, veloc = -1.73, height = 7.61
Time t = 10.0, veloc = -2.71, height = 7.34
Time t = 10.1, veloc = -3.69, height = 6.96
Time t = 10.2, veloc = -4.67, height = 6.49
Time t = 10.3, veloc = -5.65, height = 5.92
Time t = 10.4, veloc = -6.63, height = 5.25
Time t = 10.5, veloc = -7.61, height = 4.49
Time t = 10.6, veloc = -8.59, height = 3.62
Time t = 10.7, veloc = -9.57, height = 2.66
Time t = 10.8, veloc = -10.55, height = 1.60
Time t = 10.9, veloc = -11.53, height = 0.44
Time t = 11.0, veloc = -12.51, height = 0.00
Time t = 11.1, veloc = 10.28, height = 1.02
Time t = 11.2, veloc = 9.30, height = 1.95
Time t = 11.3, veloc = 8.32, height = 2.78
Time t = 11.4, veloc = 7.34, height = 3.51
Time t = 11.5, veloc = 6.36, height = 4.14
Time t = 11.6, veloc = 5.38, height = 4.67
Time t = 11.7, veloc = 4.40, height = 5.11
Time t = 11.8, veloc = 3.42, height = 5.44
Time t = 11.9, veloc = 2.44, height = 5.68
Time t = 12.0, veloc = 1.46, height = 5.82
Time t = 12.1, veloc = 0.48, height = 5.87
Time t = 12.2, veloc = -0.50, height = 5.81
Time t = 12.3, veloc = -1.48, height = 5.66
Time t = 12.4, veloc = -2.46, height = 5.41
Time t = 12.5, veloc = -3.44, height = 5.06
Time t = 12.6, veloc = -4.42, height = 4.61
Time t = 12.7, veloc = -5.40, height = 4.07
Time t = 12.8, veloc = -6.38, height = 3.43
Time t = 12.9, veloc = -7.36, height = 2.69
Time t = 13.0, veloc = -8.34, height = 1.85
Time t = 13.1, veloc = -9.32, height = 0.91
Time t = 13.2, veloc = -10.30, height = 0.00
Time t = 13.3, veloc = 8.29, height = 0.82
Time t = 13.4, veloc = 7.31, height = 1.55
Time t = 13.5, veloc = 6.33, height = 2.18
Time t = 13.6, veloc = 5.35, height = 2.71
Time t = 13.7, veloc = 4.37, height = 3.14
Time t = 13.8, veloc = 3.39, height = 3.47
Time t = 13.9, veloc = 2.41, height = 3.71
Time t = 14.0, veloc = 1.43, height = 3.85
Time t = 14.1, veloc = 0.45, height = 3.89
Time t = 14.2, veloc = -0.53, height = 3.83
Time t = 14.3, veloc = -1.51, height = 3.67
Time t = 14.4, veloc = -2.49, height = 3.42
Time t = 14.5, veloc = -3.47, height = 3.07
Time t = 14.6, veloc = -4.45, height = 2.62
Time t = 14.7, veloc = -5.43, height = 2.07
Time t = 14.8, veloc = -6.41, height = 1.42
Time t = 14.9, veloc = -7.39, height = 0.68
Time t = 15.0, veloc = -8.37, height = 0.00
Time t = 15.1, veloc = 6.56, height = 0.65
Time t = 15.2, veloc = 5.58, height = 1.20
Time t = 15.3, veloc = 4.60, height = 1.66
Time t = 15.4, veloc = 3.62, height = 2.01
Time t = 15.5, veloc = 2.64, height = 2.27
Time t = 15.6, veloc = 1.66, height = 2.43
Time t = 15.7, veloc = 0.68, height = 2.50
Time t = 15.8, veloc = -0.30, height = 2.46
Time t = 15.9, veloc = -1.28, height = 2.33
Time t = 16.0, veloc = -2.26, height = 2.10
Time t = 16.1, veloc = -3.24, height = 1.77
Time t = 16.2, veloc = -4.22, height = 1.34
Time t = 16.3, veloc = -5.20, height = 0.81
Time t = 16.4, veloc = -6.18, height = 0.19
Time t = 16.5, veloc = -7.16, height = 0.00
Time t = 16.6, veloc = 5.47, height = 0.54
Time t = 16.7, veloc = 4.49, height = 0.99
Time t = 16.8, veloc = 3.51, height = 1.33
Time t = 16.9, veloc = 2.53, height = 1.58
Time t = 17.0, veloc = 1.55, height = 1.73
Time t = 17.1, veloc = 0.57, height = 1.78
Time t = 17.2, veloc = -0.41, height = 1.74
Time t = 17.3, veloc = -1.39, height = 1.59
Time t = 17.4, veloc = -2.37, height = 1.35
Time t = 17.5, veloc = -3.35, height = 1.01
Time t = 17.6, veloc = -4.33, height = 0.57
Time t = 17.7, veloc = -5.31, height = 0.03
Time t = 17.8, veloc = -6.29, height = 0.00
Time t = 17.9, veloc = 4.68, height = 0.46
Time t = 18.0, veloc = 3.70, height = 0.83
Time t = 18.1, veloc = 2.72, height = 1.10
Time t = 18.2, veloc = 1.74, height = 1.27
Time t = 18.3, veloc = 0.76, height = 1.34
Time t = 18.4, veloc = -0.22, height = 1.31
Time t = 18.5, veloc = -1.20, height = 1.19
Time t = 18.6, veloc = -2.18, height = 0.96
Time t = 18.7, veloc = -3.16, height = 0.64
Time t = 18.8, veloc = -4.14, height = 0.22
Time t = 18.9, veloc = -5.12, height = 0.00
Time t = 19.0, veloc = 3.63, height = 0.36
Time t = 19.1, veloc = 2.65, height = 0.62
Time t = 19.2, veloc = 1.67, height = 0.78
Time t = 19.3, veloc = 0.69, height = 0.84
Time t = 19.4, veloc = -0.29, height = 0.81
Time t = 19.5, veloc = -1.27, height = 0.68
Time t = 19.6, veloc = -2.25, height = 0.45
Time t = 19.7, veloc = -3.23, height = 0.12
Time t = 19.8, veloc = -4.21, height = 0.00
Time t = 19.9, veloc = 2.81, height = 0.28
Time t = 20.0, veloc = 1.83, height = 0.45
Time t = 20.1, veloc = 0.85, height = 0.54
Time t = 20.2, veloc = -0.13, height = 0.52
Time t = 20.3, veloc = -1.11, height = 0.40
Time t = 20.4, veloc = -2.09, height = 0.19
Time t = 20.5, veloc = -3.07, height = 0.00
Time t = 20.6, veloc = 1.78, height = 0.17
Time t = 20.7, veloc = 0.80, height = 0.25
Time t = 20.8, veloc = -0.18, height = 0.23
Time t = 20.9, veloc = -1.16, height = 0.10
Time t = 21.0, veloc = -2.14, height = 0.00
Time t = 21.1, veloc = 0.95, height = 0.09
Time t = 21.2, veloc = -0.03, height = 0.08
Time t = 21.3, veloc = -1.01, height = 0.00
Time t = 21.4, veloc = -0.07, height = 0.00
事实上，稍加修改就可以得到更清晰的"图形"视图。更改程序的初始部分如下：
#include <stdio.h>
#include <unistd.h>
static void outData (double h, double v, int t) {
sleep (1);
printf ("Time t = %4d.%d: ", t / 10, t % 10);
int ih = h;
while (ih-- > 0) putchar (' ');
puts ("*");
}
该程序显示：
Time t = 0.0: *
Time t = 0.0: *
Time t = 0.1: *
Time t = 0.2: *
Time t = 0.3: *
Time t = 0.4: *
Time t = 0.5: *
Time t = 0.6: *
Time t = 0.7: *
Time t = 0.8: *
Time t = 0.9: *
Time t = 1.0: *
Time t = 1.1: *
Time t = 1.2: *
Time t = 1.3: *
Time t = 1.4: *
Time t = 1.5: *
Time t = 1.6: *
Time t = 1.7: *
Time t = 1.8: *
Time t = 1.9: *
Time t = 2.0: *
Time t = 2.1: *
Time t = 2.2: *
Time t = 2.3: *
Time t = 2.4: *
Time t = 2.5: *
Time t = 2.6: *
Time t = 2.7: *
Time t = 2.8: *
Time t = 2.9: *
Time t = 3.0: *
Time t = 3.1: *
Time t = 3.2: *
Time t = 3.3: *
Time t = 3.4: *
Time t = 3.5: *
Time t = 3.6: *
Time t = 3.7: *
Time t = 3.8: *
Time t = 3.9: *
Time t = 4.0: *
Time t = 4.1: *
Time t = 4.2: *
Time t = 4.3: *
Time t = 4.4: *
Time t = 4.5: *
Time t = 4.6: *
Time t = 4.7: *
Time t = 4.8: *
Time t = 4.9: *
Time t = 5.0: *
Time t = 5.1: *
Time t = 5.2: *
Time t = 5.3: *
Time t = 5.4: *
Time t = 5.5: *
Time t = 5.6: *
Time t = 5.7: *
Time t = 5.8: *
Time t = 5.9: *
Time t = 6.0: *
Time t = 6.1: *
Time t = 6.2: *
Time t = 6.3: *
Time t = 6.4: *
Time t = 6.5: *
Time t = 6.6: *
Time t = 6.7: *
Time t = 6.8: *
Time t = 6.9: *
Time t = 7.0: *
Time t = 7.1: *
Time t = 7.2: *
Time t = 7.3: *
Time t = 7.4: *
Time t = 7.5: *
Time t = 7.6: *
Time t = 7.7: *
Time t = 7.8: *
Time t = 7.9: *
Time t = 8.0: *
Time t = 8.1: *
Time t = 8.2: *
Time t = 8.3: *
Time t = 8.4: *
Time t = 8.5: *
Time t = 8.6: *
Time t = 8.7: *
Time t = 8.8: *
Time t = 8.9: *
Time t = 9.0: *
Time t = 9.1: *
Time t = 9.2: *
Time t = 9.3: *
Time t = 9.4: *
Time t = 9.5: *
Time t = 9.6: *
Time t = 9.7: *
Time t = 9.8: *
Time t = 9.9: *
Time t = 10.0: *
Time t = 10.1: *
Time t = 10.2: *
Time t = 10.3: *
Time t = 10.4: *
Time t = 10.5: *
Time t = 10.6: *
Time t = 10.7: *
Time t = 10.8: *
Time t = 10.9: *
Time t = 11.0: *
Time t = 11.1: *
Time t = 11.2: *
Time t = 11.3: *
Time t = 11.4: *
Time t = 11.5: *
Time t = 11.6: *
Time t = 11.7: *
Time t = 11.8: *
Time t = 11.9: *
Time t = 12.0: *
Time t = 12.1: *
Time t = 12.2: *
Time t = 12.3: *
Time t = 12.4: *
Time t = 12.5: *
Time t = 12.6: *
Time t = 12.7: *
Time t = 12.8: *
Time t = 12.9: *
Time t = 13.0: *
Time t = 13.1: *
Time t = 13.2: *
Time t = 13.3: *
Time t = 13.4: *
Time t = 13.5: *
Time t = 13.6: *
Time t = 13.7: *
Time t = 13.8: *
Time t = 13.9: *
Time t = 14.0: *
Time t = 14.1: *
Time t = 14.2: *
Time t = 14.3: *
Time t = 14.4: *
Time t = 14.5: *
Time t = 14.6: *
Time t = 14.7: *
Time t = 14.8: *
Time t = 14.9: *
Time t = 15.0: *
Time t = 15.1: *
Time t = 15.2: *
Time t = 15.3: *
Time t = 15.4: *
Time t = 15.5: *
Time t = 15.6: *
Time t = 15.7: *
Time t = 15.8: *
Time t = 15.9: *
Time t = 16.0: *
Time t = 16.1: *
Time t = 16.2: *
Time t = 16.3: *
Time t = 16.4: *
Time t = 16.5: *
Time t = 16.6: *
Time t = 16.7: *
Time t = 16.8: *
Time t = 16.9: *
Time t = 17.0: *
Time t = 17.1: *
Time t = 17.2: *
Time t = 17.3: *
Time t = 17.4: *
Time t = 17.5: *
Time t = 17.6: *
Time t = 17.7: *
Time t = 17.8: *
Time t = 17.9: *
Time t = 18.0: *
Time t = 18.1: *
Time t = 18.2: *
Time t = 18.3: *
Time t = 18.4: *
Time t = 18.5: *
Time t = 18.6: *
Time t = 18.7: *
Time t = 18.8: *
Time t = 18.9: *
Time t = 19.0: *
Time t = 19.1: *
Time t = 19.2: *
Time t = 19.3: *
Time t = 19.4: *
Time t = 19.5: *
Time t = 19.6: *
Time t = 19.7: *
Time t = 19.8: *
Time t = 19.9: *
Time t = 20.0: *
Time t = 20.1: *
Time t = 20.2: *
Time t = 20.3: *
Time t = 20.4: *
Time t = 20.5: *
Time t = 20.6: *
Time t = 20.7: *
Time t = 20.8: *
Time t = 20.9: *
Time t = 21.0: *
Time t = 21.1: *
Time t = 21.2: *
Time t = 21.3: *
Time t = 21.4: *
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