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# PROBLEM 2

#

# Modify the trajectory function below to

# plot the trajectory of several particles.

# Each trajectory starts at the point (0,0)

# given initial speed in the direction

# specified by the angle. Use the Forward

# Euler Method to accomplish this.

import math

import matplotlib.pyplot

import numpy

#from udacityplots import *

h = 0.1 # s

g = 9.81 # m / s2

acceleration = numpy.array([0., -g])

initial_speed = 20. # m / s

#@show_plot

def trajectory():

angles = numpy.linspace(20., 70., 6)

print(angles)

num_steps = 30

x = numpy.zeros([num_steps + 1, 2])

v = numpy.zeros([num_steps + 1, 2])

for angle in angles:

print(angle)

h_vel = math.cos(angle/360*2*math.pi)*initial_speed

v[0,1] = math.sin(angle/360*2*math.pi)*initial_speed

for step in range(num_steps):

# t[step + 1] = h * (step + 1)

x[step + 1,1] = x[step,1] + h * v[step,1]

v[step + 1,1] = v[step,1] - h * g

x[step + 1,0] = x[step,0] + h * h_vel

print(x)

matplotlib.pyplot.plot(x[:, 0], x[:, 1])

matplotlib.pyplot.axis('equal')

axes = matplotlib.pyplot.gca()

axes.set_xlabel('Horizontal position in m')

axes.set_ylabel('Vertical position in m')

matplotlib.pyplot.show()

# return x, v

trajectory()