TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

Prerequisites

The two problems are independent of one another, but both require only differential calculus and an introduction to projectile motion.

Time allotment - time management

At least one week out of class with some time in class for questions.

Expectations

Future payoffs

Extensions

We have made some limiting assumptions:

The easiest to consider first is the assumption of launch height. We assumed launching at 3 feet. The solution is, however, dependent on launch height. Students should determine how sensitive the solution is to launch height over the reasonable ranges of launch height, say 0 < launch height < 6.

Another thing to more carefully consider is how to choose the optimum fence heights when considering all possible launch angles. There is no single correct answer to this. However, this gives students the opportunity to try their hand at modeling and arguing on a mathematical (and possibly aesthetic basis) for their particular design.

Finally, wind resistance may play a role. But how much? To find out, assume that wind resistance is proportional to velocity and see how sensitive the solutions are to the drag coefficient.

References and Sources