Question

A man standing on a road holds his umbrella at ${30}^{\circ }$ 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 respect to the road will be

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

Answer 1

The correct option is B 20 km/hr

When the man is at rest w.r.t the 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 rain with respect to the ground
${\overrightarrow{v}}_{mg}$ = velocity of the main with respect to the ground
and ${\overrightarrow{v}}_{rm}$ = velocity of the rain with respect to the man.
We have ${\overrightarrow{v}}_{rg}$ = ${\overrightarrow{v}}_{rm}$ + ${\overrightarrow{v}}_{mg}$ ... (i)
${\overrightarrow{v}}_{rg}$ sin ${30}^{\circ }$= ${\overrightarrow{v}}_{mg}$ = 10 km/hr
or ${\overrightarrow{v}}_{rg}$ = $\frac{10}{sin{30}^{\circ }}$ = 20 km/hr