Why do this problem?
This problem links three fundamental parts of mechanics:
dimensional analysis, kinematics and coefficients of restitution.
Students will gain understanding of how equations are made. They
will apply dimensional analysis in a meaningful context. The
interesting situation will provide interest for the topic of
kinematics. The context is sufficiently rich to allow extrapolation
by the able student.
Students could be given time to look at form of the possible
equations. Although they might look complicated, the complexity is
Then students could be encouraged to consider work out which
equations might not work. They should be encouraged to give their
reasons clearly. This could be done in pairs.
- What are the key features of the equations?
- What conditions must sensible physical equations satisfy?
- Are there any equations which will obviously not work?
- How would the analysis for a real bomb vary (discussion)?
- Do you think that effects of air resistance etc. will be
Students can work on the derivation of the equation. For even more
extension, they could try to analyse the 3 bounce case or even try
to work out the effects of an infinite number of bounces.
Students struggling could try the first question Dam
If they are struggling on the dimensional analysis part then
you could ask them to work out the dimensions of g and velocities