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("\nDistance 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("\nDistance 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()
