# Common physics equations determine the x and y coordinates of a projectile object at any time 
# Given the object's initial veocity and angle at time 0 with the initial position of x = 0 and y = 0 

# The equation for x is v * t * cos(a). 
#The equation for y is v * t * sin(a) - 0.5 * g * t * t.

# The program's code asks the user for the object's initial veocity, angle, and height(y position), and prints the objects's position for every second 
#Until the object's y position is no longer greater than 0 (meaning the object fell back to Earth)

import math 

def trajectory(t, a, v, g, h): 
    """Calculates  new x, y position"""
    x = y * t * math.cos(a)
    y = h + v * t * math.sin(a) - 0.5 * g * t * t
    return(x,y)


def degree_to_radians(degrees): 
    """Converts degrees to radians"""
    return((degrees * math.pi) / 180.0)

gravity = 9.81 #Earth gravity (m/s^2)
time = 1.0 # time(s)
x_loc = 0
h = 0 

angle = float(input('Launch angle (deg):'))
print(angle)
angle = degree_to_radians(angle)

velocity = float(input('Launch velocity (m/s): '))
print(velocity)

height = float(input('Initial height (m): '))
y_loc = height 
print(y_loc)

while ( y_loc >= 0.0 ): 
    print(f'Time {time:3.0f} x = {x_loc:3.0f} y = {y_loc:3.0f}')
    x_loc, y_loc = trajectory(time, angle, velocity, gravity, height)
    time += 1.0