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("
Distance 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("
Distance 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()