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Laws Of Motion

Question
CBSEENPH11017006

A cyclist goes round the track of length 440m in 22s. Find the angle that the cyclist makes with the vertical.

Solution
Let r be the radius of track and v the speed of cyclist while circling  the track.
Here,
Total length of track = 440m.
Therefore,
                         2 πr equals 440 
rightwards double arrow                        r equals 70 straight m
Time taken to complete the track is 22 s.
Therefore,
                  v equals fraction numerator italic 2 pi r over denominator t end fraction equals 440 over 22 equals 20 space straight m divided by straight s 
Now,     tan theta space equals space fraction numerator v squared over denominator r g end fraction equals fraction numerator left parenthesis 20 right parenthesis squared over denominator 70 cross times 9.8 end fraction equals 0.583 
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#6 {main}</pre>, is the angle that the cyclist makes with the vertical.