This activity is designed to be accessible to A-level maths students (Key Stage 5).

Detailed teachers' notes for this activity are available on our NRICH website.

Pole Vaulting

Stage: 5 Challenge Level: Challenge Level:1

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.

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

Further information

Detailed teachers' notes for this activity are available on our NRICH website.

Our article High Jumping by Professor John Barrow explores how mathematics helps athletes optimise performance in the high jump and pole vault.