A cyclist riding at a speed of 10 m/s, takes a turn round the circular track. For the safe turn he bends at angle 30° with the vertical. Find the radius of track.

Solution

Speed of the cyclist, v = 10 m/s
Angle at which the cyclist bends = 30^o
We know that,

tan space theta space equals space fraction numerator v squared over denominator r g end fraction T h a t space i s comma space t a n space 30 to the power of o space equals space fraction numerator 10 space cross times space 10 over denominator r space cross times space 9.8 space end fraction r space equals space fraction numerator 10 space cross times space 10 space x space square root of 3 over denominator 9.8 end fraction space equals space 17.6 space m

The radius of the circular track = 17.6 m.

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