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）

 #from math import pi,sin,cos,radians
 import math

 def main():
     angle = eval(input("Enter the launch angle (in degrees):"))
     vel = eval(input("Enter the initial velocity (in meters/sec):"))
     h0 = eval(input("Enter the initial height (in meters):"))
     time = eval(input("Enter the time interval: "))

     xpos = 0
     ypos = h0

     theta = math.radians(angle)
     xvel = vel * math.cos(theta)
     yvel = vel * math.sin(theta)     

     while ypos >= 0:
         xpos = xpos + time * xvel
         yvell = yvel - time * 9.8
         ypos = ypos + time * (yvel + yvell)/2.0
         yvel = yvell

     print("\nDistance traveled:{0:0.1f}meters.".format(xpos))

 if __name__ == "__main__":
     main()

（2）画出轨迹

 from math import pi,sin,cos,radians
 import turtle

 def drawLine(x, y):#画线
     turtle.pendown()
     turtle.goto (x, y)

 def drawText(x, y,n):
     turtle.penup()
     turtle.goto (x, y)
     turtle.pendown()
     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

 def main():
     angle = eval(input("Enter the launch angle (in degrees):"))
     vel = eval(input("Enter the initial velocity (in meters/sec):"))
     h0 = eval(input("Enter the initial height (in meters):"))
     time = eval(input("Enter the time interval: "))
     n=20#显示系数

     xpos = 0
     ypos = h0

     drawLine(500,0) #初始坐标轴
     drawLine(0,0)
     drawLine(0,300)
     drawLine(0,18)

     theta = radians(angle)
     xvel = vel * cos(theta)
     yvel = vel * sin(theta)     

     while ypos >= 0:
         xpos = xpos + time * xvel
         yvell = yvel - time * 9.8
         ypos = ypos + time * (yvel + yvell)/2.0
         yvel = yvell
         drawLine(xpos*n,ypos*n)
         drawText(xpos*n,ypos*n,n)

     turtle.hideturtle()#隐藏箭头
     print("\nDistance traveled:{0:0.1f}meters.".format(xpos))

 if __name__=="__main__":
     main()

引入turtle库，画出轨迹图

（3）程序模块化

 from math import pi,sin,cos,radians

 def getInputs():
     angle=eval(input("enter the launch angle (degree):"))
     vel = eval(input("Enter the initial velocity (in meters/sec):"))
     h0 = eval(input("Enter the initial height (in meters):"))
     time = eval(input("Enter the time interval: "))
     return angle,vel,h0,time

 def getXYComponents(vel,angle):
     theta=radians(angle)
     x=vel*cos(theta)
     y=vel*sin(theta)
     return x,y

 def updatePosition(time,xpos,ypos,xvel,yvel):
     xpos=xpos+time*xvel
     yvell=yvel-9.8*time
     ypos=ypos+(yvell+yvel)*time/2
     yvel=yvell
     return xpos,ypos,yvel

 def main():
     angle,vel,h0,time=getInputs()
     xvel,yvel=getXYComponents(vel,angle)
     xpos,ypos=0,h0
     while ypos>=0:
         xpos,ypos,yvel=updatePosition(time,xpos,ypos,xvel,yvel)
     print("distance traveled:{0:0.1f}meters.".format(xpos))

 if __name__=="__main__":
     main()