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 $10\text{km/hr}$. 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 $20\text{km/hr}$

When the man is at rest w.r.t 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.

Let,
${\overrightarrow{v}}_{rg}=$ 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

From the question,

${\overrightarrow{v}}_{rg}\sin {30}^{\circ }={\overrightarrow{v}}_{mg}=10\text{km/hr}$

$\therefore {\overrightarrow{v}}_{rg}=\frac{10}{\sin {30}^{\circ }}=20\text{km/hr}$

Hence, option $\left(\text{B}\right)$ is correct.