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### Number and algebra

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### Working mathematically

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# Cannon Balls

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Age 16 to 18

ShortChallenge Level

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?

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?

A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?