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Lunar Leaper

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

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Whirlyball

Whirl a conker around in a horizontal circle on a piece of string. What is the smallest angular speed with which it can whirl?

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Bridge Builder

In this short problem we investigate the tensions and compressions in a framework made from springs and ropes.

Cannon Balls

Stage: 5 Short Challenge Level: Challenge Level:1
 

A cannon ball is fired vertically upwards into the air. How fast would it have to be fired to take 1 second to land?

How fast would it have to be fired to take 10, 100, 1,000 or 1,000,000 seconds to land?

What would be the highest point of the ball in each case?

(Assume that gravity is a constant 10ms$^{-2}$ in your calculations.)
 

Given that the radius of the earth is about 6000km, which of your calculations would give a good approximation to reality? At what speed would the approximation break down, in your opinion?

Extension activity: Suppose that the balls are fired upwards from a trampoline with coefficient of restitution 0.5. In each case, after how many bounces would the balls bounce less than 1m high? Try to make an estimate before performing a full calculation.

Extension problem: why not try the extension question Escape From Planet Earth?