Homework 4

作者：丁峰 学号：2015301020029 物基一班

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题目：

2.9. Calculate the trajectory of your cannon shell including both air drag and the
Reduced air density at high altitudes so that you can reproduce the results in
Figure2.5.Perform your calculation for different firing angles and determine the
Value of the angle that gives the maximum range.

解答：

$$x_{i+1}=x_i+v_{x,i}\Delta t$$
$$v_{x,i+1}=v_{x,i}-\frac{F_{drag,x}}{m}*\Delta t$$
$$y_{i+1}=y_i+v_{y,i}\Delta t$$
$$v_{y,i+1}=v_{y,i}-g\Delta t-\frac{F_{drag,y}}{m}\Delta t$$
将初始速度固定为$700m/s$
在等温情况下
考虑空气阻力由教材$P29 (2.22)(2.23)$可得
$$\rho=\rho_0e^{(-y/y0)}$$
在绝热情况下
由教材$P30 (2.24)(2.25)$可得
$$\rho=\rho_0(1-a*\frac{height}{T_0})^\alpha$$
$$F_{drag}=\frac{\rho}{\rho_0}F_{drag}(y=0)$$
代码
等温与绝热过程绘图如下

（尚未完成）考虑如何找到发射最远的角度的值
初步估计在45°左右