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Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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Far Horizon

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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Air Routes

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Alternative Record Book

Stage: 4 and 5 Challenge Level: Challenge Level:1

The 100m sprint isn't the only event where humans move fast! Here are some suggestions of other speedy competitors you could consider:

A cyclist in a sprint
A wheelchair racer in the Paralympics
A diver as he enters the water
A long jumper as he takes off
or perhaps including the Winter Olympics too...