Python——铅球飞行计算问题

一、

1、IPO描述为：
输入：铅球发射角度、初始速度(m/s)、初始高度(m)

处理：模拟铅球飞行，时刻更新铅球在飞行中的位置

输出：铅球飞行距离(m)

可以拆分小的时间段。任意时刻的位置，都是由前面的位置叠加新的时间段位移引起的，最终的控制条件为，当落地时结束，即y轴坐标为0时结束。微分的思想

（1）

 1 #from math import pi,sin,cos,radians
 2 import math
 3  
 4 def main():   
 5     angle = eval(input("Enter the launch angle (in degrees):"))
 6     vel = eval(input("Enter the initial velocity (in meters/sec):"))
 7     h0 = eval(input("Enter the initial height (in meters):"))
 8     time = eval(input("Enter the time interval: "))
 9  
10     xpos = 0
11     ypos = h0
12  
13     theta = math.radians(angle)
14     xvel = vel * math.cos(theta)
15     yvel = vel * math.sin(theta)     
16  
17     while ypos >= 0:
18         xpos = xpos + time * xvel
19         yvell = yvel - time * 9.8
20         ypos = ypos + time * (yvel + yvell)/2.0
21         yvel = yvell
22         
23     print("
Distance traveled:{0:0.1f}meters.".format(xpos))
24      
25 if __name__ == "__main__":
26     main()

（2）画出轨迹

 1 from math import pi,sin,cos,radians
 2 import turtle
 3 
 4 def drawLine(x, y):#画线
 5     turtle.pendown()
 6     turtle.goto (x, y)
 7 
 8 def drawText(x, y,n):
 9     turtle.penup()
10     turtle.goto (x, y)
11     turtle.pendown()
12     turtle.write((float("%2.f"%x)/n,float("%2.f"%y)/n))#注意表达方式，只保留两位小数
13 
14 def main():   
15     angle = eval(input("Enter the launch angle (in degrees):"))
16     vel = eval(input("Enter the initial velocity (in meters/sec):"))
17     h0 = eval(input("Enter the initial height (in meters):"))
18     time = eval(input("Enter the time interval: "))
19     n=20#显示系数
20  
21     xpos = 0
22     ypos = h0
23 
24     drawLine(500,0) #初始坐标轴
25     drawLine(0,0)
26     drawLine(0,300)
27     drawLine(0,18)
28  
29     theta = radians(angle)
30     xvel = vel * cos(theta)
31     yvel = vel * sin(theta)     
32  
33     while ypos >= 0:
34         xpos = xpos + time * xvel
35         yvell = yvel - time * 9.8
36         ypos = ypos + time * (yvel + yvell)/2.0
37         yvel = yvell
38         drawLine(xpos*n,ypos*n)
39         drawText(xpos*n,ypos*n,n)
40         
41     turtle.hideturtle()#隐藏箭头
42     print("
Distance traveled:{0:0.1f}meters.".format(xpos))
43 
44 
45 if __name__=="__main__":
46     main()

引入turtle库，画出轨迹图

（3）程序模块化

 1 from math import pi,sin,cos,radians
 2 
 3 def getInputs():
 4     angle=eval(input("enter the launch angle (degree):"))
 5     vel = eval(input("Enter the initial velocity (in meters/sec):"))
 6     h0 = eval(input("Enter the initial height (in meters):"))
 7     time = eval(input("Enter the time interval: "))
 8     return angle,vel,h0,time
 9 
10 def getXYComponents(vel,angle):
11     theta=radians(angle)
12     x=vel*cos(theta)
13     y=vel*sin(theta)
14     return x,y
15 
16 def updatePosition(time,xpos,ypos,xvel,yvel):
17     xpos=xpos+time*xvel
18     yvell=yvel-9.8*time
19     ypos=ypos+(yvell+yvel)*time/2
20     yvel=yvell
21     return xpos,ypos,yvel
22 
23 def main():
24     angle,vel,h0,time=getInputs()
25     xvel,yvel=getXYComponents(vel,angle)
26     xpos,ypos=0,h0
27     while ypos>=0:
28         xpos,ypos,yvel=updatePosition(time,xpos,ypos,xvel,yvel)
29     print("distance traveled:{0:0.1f}meters.".format(xpos))
30 
31 if __name__=="__main__":
32     main()