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Question

The maximum speed of a cyclist on a race track is 20 m/s and he can bend to a maximum angle of 45. The race track has a curve of radius 20 m. Is this race track safe for the racer? If not, what should be the angle of banking of the curve?
[Take tan1(2)=63.43]

A
The track is safe.
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B
The track is not safe, 19
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C
The track is not safe, 10
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D
The track is not safe, 15
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Solution

The correct option is B The track is not safe, 19
Velocity of cyclist =v=20 m/s
Radius of curve =r=20 m

If the cyclist turns on this curve at a speed of 20 m/s, then
tanθ=v2rg=20220×10=2
θ=tan12=63.43

The required angle of bending of the cyclist is more than the maximum amount of bending that the cyclist can do. Hence the track is not safe for the cyclist.

Therefore, the track should be provided with a banking of 63.4345=18.4319

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