# Exercise 2

## calculate the height of a ball

Given parabolic flight, the height of a ball \(y\) 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 size of the initial velocity vector (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 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: 9.8 enter a value for v0: 6.789 enter a value for theta: 0.123 enter a value for x: 4.5 enter a value for y0: 5.4 The vertical height of the ball is: 3.77057803072