Question

A man standing on a road hold his umbrella at ${30}^0$ with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km / hr. He finds that raindrops are hitting his head vertically, the speed of raindrops with respects to the road will be -

• A. 10 km / hr
• B. 20 km / hr
• C. 30 km / hr
• D. 40 km / hr

Answer 1

Answer: (B)

20 km / hr

When the man is at rest w.r.t. the ground, the rain comes to him at an angle ${30}^o$ with the vertical. This is the direction of the velocity of raindrops with respect to the ground.
Here ${\overrightarrow{V}}_{rg}=$ velocity of rain with respect to the ground.
${\overrightarrow{V}}_{mg}=$ velocity of man with respect to the ground.
and ${\overrightarrow{V}}_{mn}=$ velocity of rain with respect to the man.
We have ${\overrightarrow{V}}_{rg}={\overrightarrow{V}}_{rm}+{\overrightarrow{V}}_{mg}$........(i)
Taking horizontal components equation (i) gives.

$V_{rg}sin{30}^o=V_{mg}=10lm/hr$

or $V_{rg}=\frac{10}{sin{30}^o}=20km/hr$