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# Illusion

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Age 11 to 16

Challenge Level

- Problem
- Student Solutions

A security camera, which takes one picture each half a second, films a cyclist going by at 8.5 miles per hour on a bike which has wheels of diameter 24 inches. There is a reflector fixed to the spokes of each wheel of the bike. Explain why it is that, in the film, the cyclist appears to go forward while the wheels appear to go backwards. If the cyclist goes a little faster the wheels appear to be stationary. At what speed does this happen?

You will need to know that 1 mile = 1760 yards, 1 yard = 3 feet and 1 foot = 12 inches to do this question. Can you also change the numbers (not necessarily by direct conversion) to pose a similar problem in metric units?