Question

A man standing on a road has to hold his umbrella at ${30}^{\circ }$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10{\text{kmh}}^{-1}$ . He finds that raindrops are hitting his head vertically. The actual speed of raindrops is

• A. $20{\text{kmh}}^{-1}$
• B. $10\sqrt{2}{\text{kmh}}^{-1}$
• C. $20\sqrt{3}{\text{kmh}}^{-1}$
• D. $10{\text{kmh}}^{-1}$

Answer 1

The correct option is A $20{\text{kmh}}^{-1}$

When the man is at rest with respect to the ground, the rain comes to him at an angle ${30}^{\circ }$ with the vertical. This is the direction of the velocity of raindrops with respect to the ground.

Here, $\overrightarrow{v_{rg}}=$ velocity of the rain w.r.t. the ground and $\overrightarrow{v_{mg}}$ is the velocity of man w.r.t. the ground.



From figure,
$\sin {30}^{\circ }=\frac{|\overrightarrow{v_{mg}}|}{|\overrightarrow{v_{rg}}|}$
or $|\overrightarrow{v_{rg}}|=\frac{|\overrightarrow{v_{mg}}|}{\sin {30}^{\circ }}$
$=\frac{10}{1/2}=20{\text{kmh}}^{-1}$