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Question
A cyclist riding a bicycle at a speed of `14sqrt3` m/s takes a turn around a circular road of radius `20sqrt3` m without skidding. Given g = 9.8 m/s2, what is his inclination to the vertical ______.
Options
30°
45°
60°
90°
Solution
A cyclist riding a bicycle at a speed of `14sqrt3` m/s takes a turn around a circular road of radius `20sqrt3` m without skidding. Given g = 9.8 m/s2, what is his inclination to the vertical 60°.
Explanation:
`v^2 = (14sqrt3)^2 = 14^2xx3 = 196xx3=588`
`rg=(20sqrt3)xx9.8 = 20xx9.8xxsqrt3 = 196sqrt3`
`v^2/rg = 588/(196sqrt3) = 588/196xx1/sqrt3`
`=3xx1/sqrt3 = sqrt3`
`theta = tan^-1 (sqrt3)`
`tan60° = sqrt3`
θ = 60∘
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