### 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

##### Stage: 5 Challenge Level:

The pole vault event consists of these phases:

1. The vaulter stands at the end of the runway holding the pole vertically.
2. The runner sprints along the runway as the top of the pole is moved towards the ground.
3. The pole is planted in the box.
4. The pole flexes and absorbs the energy of the runner.
5. The pole straightens and the runner is propelled up and (hopefully!) over the bar.

This is a fascinating mechanical process!

Can you draw a sequence of simple pictures which represent the stages of a pole vault?

Then consider these questions, using appropriate data for the athlete:

1. What is the locus of the centre of mass of the athlete during this process?
2. How much kinetic energy does the runner and pole contain just prior to planting in the box?
3. How efficiently is this converted into potential energy?

There are various levels of sophistication at which this can be considered - analyse with as much depth as you feel is relevant and you can use real data (some are provided below) or approximations. Either is fine, provided that your assumptions and estimations are clearly stated.

NOTES AND BACKGROUND
You might wish to use the following data:

Pole vaulting world record holders as of January 2011:

Male = 6.14m (Sergey Bubka), Female = 5.06m (Yelena Isinbayeva)

Lengths of poles vary between 2.3m to 6.4m, with weight rated individually

Height and weight of vaulters: Sergey Bubka 1.83m/80kg, Yelena Isinbayeva 1.74m/65kg

Length of runway: 40m