Running and Hopping Activity

This exercise (pdf here) is a variation on a traditional textbook exercise using derivatives, but students have to collect their own data in order to solve the problem. The task is to determine the ideal trajectory if you want to go from one corner of a soccer field to the opposite corner, with the limitation that you can run along the side, but before you cross, your feet will be tied together and you will hop the rest of the way.

Students form groups. One of them will be the runner. The information students need to collect are:
- the velocity of the runner as he runs.
- the velocity of the runner when he hops.
- the time it takes to tie the runners feet.
- the length and width of the soccer field.

The rest is an optimization problem, using the Chain rule.

Notes:
- Students don't necessarily realize that they won't need to run and hop all the way.
- Measurements of the field can easily be found using GoogleEarth for example, rather than physically doing it.
- The time it takes to tie the runner's legs doesn't influence the answer to "what is the quickest path?" since it is a constant.

                                                    (download the pdf)