Parabolic Flight

Given parabolic flight, the height y of a ball is given by the equation:

\begin{equation} y = x \tan(\theta) - \left[ \frac{1}{2 v_{0}^{2}} \right] \left[ \frac{g x^{2}}{cos(\theta)^{2}} \right] + y_{0} \end{equation}

where x is a horizontal coordinate (metres), g is the acceleration of gravity (metres per second per second), v_{0} is the initial velocity (metres per second) at an angle \theta (radians) with the x-axis, and (0,y_{0}) is the initial position of the ball (metres).

Write a program to compute the vertical height y of a ball. The program should ask the user to input values for g, v_{0}, \theta, x, and y_{0}, and print out a sentence giving the vertical height of the ball.

Test your program with this example:

enter a value for g (m/s/s): 9.8
enter a value for v0 (m/s): 6.789
enter a value for theta (rad): 0.123
enter a value for x (m): 4.5
enter a value for y0 (m): 5.4
The vertical height of the ball is:  3.77057803072 m

In Python to use cos() and tan() you will have to import the math package:

import math

and then you can use math.cos() and math.tan().