Question

The maximum speed of a cyclist on a race track is $20\text{m/s}$ and he can bend to a maximum angle of ${45}^{\circ }$. The race track has a curve of radius $20\text{m}$. Is this race track safe for the racer? If not, what should be the angle of banking of the curve?
[Take ${\tan }^{-1}\left(2\right)={63.43}^{\circ }$]

• A. The track is safe.
• B. The track is not safe, ${19}^{\circ }$
• C. The track is not safe, ${10}^{\circ }$
• D. The track is not safe, ${15}^{\circ }$

Answer 1

The correct option is B The track is not safe, ${19}^{\circ }$

Velocity of cyclist $=v=20\text{m/s}$
Radius of curve $=r=20\text{m}$

If the cyclist turns on this curve at a speed of $20\text{m/s}$, then
$\tan \theta =\frac{v^2}{rg}=\frac{{20}^2}{20\times 10}=2$
$\Rightarrow \theta ={\tan }^{-1}2={63.43}^{\circ }$

The required angle of bending of the cyclist is more than the maximum amount of bending that the cyclist can do. Hence the track is not safe for the cyclist.

Therefore, the track should be provided with a banking of $63.{43}^{\circ }-{45}^{\circ }=18.{43}^{\circ }\approx {19}^{\circ }$