Question

A cyclist goes round a circular track $440m$ long in $20second$. What is the angle that his cycle makes with the vertical to safely cover the circular track?

• A. ${35}^{\circ }{12}^{\prime }$
• B. ${40}^{\circ }{12}^{\prime }$
• C. ${20}^{\circ }{12}^{\prime }$
• D. ${15}^{\circ }{12}^{\prime }$

Answer 1

The correct option is A ${35}^{\circ }{12}^{\prime }$

Circumference$2\pi R=440R=\frac{440}{2\pi }=\frac{220}{\pi }m$

Speed $v=\frac{2\pi R}{20}=\frac{440}{20}=22m/sN\cos \theta =mg$

and $N\sin \theta =\frac{m{v}^2}{R}$

Dividing these two equations:

$\tan \theta =\frac{v^2}{Rg}=\frac{220\times 22}{220\times 10}\pi =0.69\theta ={tan}^{-1}\left(0.69\right)\cong 35°$