AMS326HW3Q1Spring2020.py

#Ryan Burgert AMS326 HW3 Q1 Spring 2020
#My solution uses euler's method
#Results:
#	Total travel time for vB = 7  is 4814.712
#	Total travel time for vB = 14 is 822.863
#	Total travel time for vB = 21 is 441.819

from math import cos,sqrt
from rp import *

def w(v0,x,a):
	return 4*v0*(x/a-x**2/a**2)

def x_vel(vB,x,y):
	return -vB*(x/sqrt(x**2+y**2))

def y_vel(vB,x,y,v0,a):
	return -vB*(y/sqrt(x**2+y**2))+w(v0,x,a)

def trajectory(vB, Δt, v0=14, a=7777):
	x=a
	y=0
	yield x,y
	while x>0:
		Δx=Δt*x_vel(vB,x,y)
		Δy=Δt*y_vel(vB,x,y,v0,a)
		x+=Δx
		y+=Δy
		yield x,y

def trial(vB, Δt=.001):
	path=list(trajectory(vB,Δt=Δt))
	t=Δt*len(path)
	print('Total travel time for vB =',vB,'is',t)
	display_path(path)
	return path

for vB in [7,14,21]:
	trial(vB)