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What is the maximum height a pole vaulter could reach?

Whilst at first this question looks difficult, once broken down it becomes quite easy. It is a simple case of energy exchange.

The pole vaulter gives themselve kinetic energy as they aproach the bar, and turn this into gravitational potential energy in order to get the height. This means we can equate the two terms for kinetic and potential energy:

1/2 m v^2 = mgh

And rearrange to give:

h = 1/2 * v^2 / g

Assuming an athlete can run at 10 m/s and take g as 10 m/s/s, the height comes out as 5m.

The question can then be extended by saying that the pole vault world record is 6.16m, so where does the extra metre come from?

An assumption has been made that the athlete is a particle acting from the centre of mass of the athlete which will be about a metre off the ground.

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