Why do this problem?
This problem provides an interesting context in which to
engage with centres of mass, potential energy and kinetic energy.
This problem is a good group task and provides a meaningful end of
mechanics module review of ideas or preparatory work for a new
mechanics module. It will be reasonably straightforward for
students to work on in a reasonably unstructured fashion and might,
therefore, be appropriate to set as cover work or for an end of
Simply pose the problem and leave students to work on the task
in small groups. As a focus for a lesson ask groups to prepare a
poster describing their answers to the three questions. Should you
wish, as a follow-up task you could as a class discuss the
differences which have arisen and try to determine a collective
'best' answer to the problem. If you are feeling adventurous then
you might wish to talk to the PE department about the physics of
pole vaulting or use digital technologies to attempt to trace
accurately the locus of a pole-vaulter as he or she makes a jump -
the context allows for varying depths of approach.
It will be easy to adapt this task to other sports: high
jumping, long jumping and diving, for example.
Key points of note
The complexity of the modelling assumptions required in this
problem is greater than the mathematics required to solve the
problem at its simplest level - this problem is not looking for a
sophisticated algebraic analysis in the first instance.
As a teacher you are not expected to know the answer to all
questions which might arise during the course of the exploration,
particularly since many will be cross-curricular in nature; you can
use your skills to help students to steer a path through the
problem and to coordinate and maximise the learning potential of
any resulting discussion.