# Exercise 2

## calculate the height of a ball

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

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

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


Paul Gribble | fall 2014