Question

The angle which the bicycle and its rider must make with the vertical when going round a curve of 7 mradius at 5 m/s is (Tan 20° = 0.364)
1)20° 2)15° 3) 10° (4)5°21

Answer 1

20°2

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Answer 2

Given:

Velocity v = 5 m/s

Radius r = 7 m

tan 20° = 0.364

To Find:

Angle made when going round a curve.

Solution:

Let α be tha angle made by the cycle and the cyclist with the vertical.

Bending of a cyclist in a circular motion is given by the following relation:

$\tan( \alpha ) = \frac{ {v}^{2} }{rg}$

$tan( \alpha ) = \frac{ {5}^{2}}{(7)(10)}$

$tan( \alpha ) = \frac{25}{70}$

$tan( \alpha ) = \frac{5}{14}$

$tan( \alpha ) = 0.36$

It is given that tan 20° = 0.364

Therefore,

$\alpha = {tan}^{ - 1}(0.36) = {20}^{0}$

The angle which the bicycle and its rider must make with the vertical when going round a curve of 7m radius at 5 m/s is 20°. Option (1) is the answer.