Question

A motor cyclist goes round a circular race course of diameter 320m at 144km/h. How far from the vertical must he lean inwards to keep his balance? Take g=10m/s

Answer 1

$tan ^{ - 1} ( \frac{1}{2} )$

Explanation:

$Given, \: \: \: v = 144 \: km {h}^{ - 1} = 144 \times \frac{5}{18} \: m {s}^{ - 1} = 40 \: m {s}^{ - 1} \: \: \: and \\ r = 320 \: m \\ we \: \: know \: \: \boxed{tan \theta = \frac{ {v}^{2} }{rg} } \\ Now, \: \: \: putting \: \: values \\ tan \theta = \frac{(40 \: m {s}^{ - 1} )^{2} }{320 \: m \times 10 \: m {s}^{ - 2} } \\ = \frac{40 \times 40}{320 \times 10} \\ = \frac{1}{2} \\ So, \: \: \: \boxed{ \theta = tan ^{ - 1} ( \frac{1}{2} )}$