Question

Rain is falling vertically with a velocity of $15m{s}^{-1}$. A person rides a bicycle with a speed of $15m{s}^{-1}$ in the west to east direction. What is the direction (angle with vertical) in which he should hold his umbrella to save himself from the rain?

• A. ${45}^{\circ }$
• B. ${90}^{\circ }$
• C. ${30}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$


The rain is falling vertically. Hence ${\theta }_r$ (angle of rain with the horizontal) is ${90}^{\circ }$.
The person is moving with a velocity of $15m/s$. Hence the rain drops fall on the person at a certain angle and not vertically. Let this angle be $\theta$. Then,
$\tan \theta =\frac{|{\overrightarrow{v}}_m|}{|{\overrightarrow{v}}_r|}=\frac{15}{15}=1$
Hence $\theta ={45}^{\circ }$