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 $10km/h$. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to the ground.

• A. $5km/h$
• B. $10km/h$
• C. $10\sqrt{2}km/h$
• D. $20km/h$

Answer 1

The correct option is D $20km/h$

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. The situation when the man runs is shown in the figure


$V_{rg}=$ velocity of rain drops with respect to ground.
$V_{man}=$ velocity of man $=10km/h$
Hence, $\cos \theta =\frac{10}{V_{rg}}$
$\Rightarrow \cos {60}^{\circ }=\frac{10}{V_{rg}}$
$\Rightarrow \frac{1}{2}=\frac{10}{V_{rg}}$
$\Rightarrow V_{rg}=20km/h$
Hence, velocity of rain drops with respect to the ground is $20km/h$.