# This program computes the trajectory of a projectile.
import math

# constant for Earth acceleration in meters/second^2
ACCELERATION = -9.81

def main():
    # explain program
    print("This program computes the")
    print("trajectory of a projectile given")
    print("its initial velocity and its")
    print("angle relative to the")
    print("horizontal.")
    print()

    # read input from user
    velocity = float(input("velocity (meters/second)? "))
    angle = math.radians(float(input("angle (degrees)? ")))
    steps = int(input("number of steps to display? "))
    print()

    x_velocity = velocity * math.cos(angle)
    y_velocity = velocity * math.sin(angle)
    total_time = -2.0 * y_velocity / ACCELERATION
    time_increment = total_time / steps
    x_increment = x_velocity * time_increment

    x = 0.0
    y = 0.0
    t = 0.0
    print("step", "x", "y", "time", sep="\t")
    for i in range(steps + 2):
        print(i, round(x, 2), round(y, 2), round(t, 2), sep="\t")
        t += time_increment
        x += x_increment
        y = y_velocity * t + 0.5 * ACCELERATION * t * t

main()