This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games. In particular, we derive the classic Hill-Keller model for a sprinter exerting ``maximum'' effort as he/she accelerates down a track.
The model includes one or more unknown parameters that must be estimated from comparison to the data. Students can then gauge the fidelity of the model to the data and validate the model by using it to predict how fast Bolt could run other distances, for which additional data is provided.
The project has two distinct parts---the first motivates the derivation of an ordinary differential equations (ODEs) as a model for a physical process, as an introduction to the subject; the second part can be tackled after the students have seen solution strategies for autonomous ODEs. At this point they can fit parameters and make predictions, which requires the use of a computer algebra system; a Maple worksheet is supplied.
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