Question

A stationary person observes that rain is falling vertically down at $18\text{km/hr}$. A cyclist is moving in positive x- direction on the level road, at $24\text{km/hr}$. At what angle from the horizontal should the cyclist hold his umbrella to protect himself from rain?

• A. ${37}^{\circ }$
• B. ${53}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is A ${37}^{\circ }$

${\overrightarrow{V}}_{rg}=0-18\hat{j}$, ${\overrightarrow{V}}_{cg}=24\hat{i}$
${\overrightarrow{V}}_{rc}={\overrightarrow{V}}_{rg}-{\overrightarrow{V}}_{cg}=-18\hat{j}-24\hat{i}$
The angle between horizontal and ${\overrightarrow{V}}_{rc}$ is
$\tan \theta =\frac{-18}{-24}=\frac{3}{4}$
$\theta ={\tan }^{-1}\left(\frac{3}{4}\right)={37}^o$