### Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

### High Jumping

How high can a high jumper jump? How can a high jumper jump higher without jumping higher? Read on...

### Wobbler

A cone is glued to a hemisphere. When you place it on a table in what position does it come to rest?

# Pole Vaulting

### 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 term activity.

### Possible approach

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.

### Possible variation

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.