# Theoretical Modeling

Developing a Numerical Model of a Bouncing Ball

Read the bouncing ball example of this textbook. Implement the code given in the example and add comments to the code to figure out what is happening. You may have to do some error correction to the code. Adjust the defined constants to match with our experiment. Note that this code starts from the terminal velocity and defines a drag coeffiecient from that assuming quadratic drag. You should adjust the code to start from the drag coefficient and calculate the terminal velocity. You may assume that quadratic drag still applies. For the drag coefficient you can either assume 0.25 (see this article and this article) by NASA or you can experimentally determine the quadratic drag coefficient using the same experiment as Experiment 1. The only constant that maybe difficult to fit is k (the "spring constant" of the ball). You can leave this as the default value for now.

Since we are dropping the ball from rest and it will only be moving in the y direction, it may make more sense to change the plot from y-position vs. x-position to y-position vs. time.

We will use this numerical description of a bouncing ball as the "true" solution that we will compare the results of all three experiments to.

Deliverable #1: Submit a print-out of your numerical code and the produced graph.