TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

Prerequisite

The prerequisite is a knowledge of the calculus that centers around the relationship between position, velocity and acceleration.

Time allotment - time management

As mentioned above, this is a problem with a certain degree of open-endedness. It is actually more of a project. It could be worked on over a period of several hours outside of class. A computer algebra system would greatly facilitate the work.

Expectations

I would expect that most students could solve this problem successfully. Some might need hints. The teacher might give some hints, or a "naive" solution. For example, consider the following lift curve. What is wrong with it? Hint: think about the derivatives.

Input := 

naive[x_] := If[ 0 <= x <= Pi, .1 Sin[x], 0]

Input := 

Plot[ naive[x], {x,0,2 Pi} ]

Output =

-Graphics-

Future payoffs

The search for the "best" solution leads directly into higher mathematics.

Extensions

A classic extension is the case where we have a rise, a high dwell, and then a drop to a low dwell. Cam design and curve fitting are really closely related.