Question

A man standing on a road has to hold his umbrella at ${30}^{\circ }$ with the vertical to keep the rain away. He then throws the umbrella and starts running at $10\text{km/h}$. He finds that rain drops are hitting his head vertically. Find the speed of rain with respect to road.

• A. $10\text{km/s}$
• B. $20\text{km/h}$
• C. $10\sqrt{3}\text{km/s}$
• D. $20\sqrt{3}\text{km/h}$

Answer 1

The correct option is B $20\text{km/h}$


${\overrightarrow{v}}_{\text{RM}}$ (velocity of rain with respect to man) is vertical downward ${\overrightarrow{v}}_{\text{RM}}={\overrightarrow{v}}_{\text{R}}-{\overrightarrow{v}}_{\text{M}}$



$|{\overrightarrow{v}}_{\text{R}}|\sin {30}^{\circ }=|{\overrightarrow{v}}_{\text{M}}|$
$\Rightarrow v_{\text{R}}=\frac{10\text{Km/hr}}{\sin {30}^{\circ }}=\frac{10\text{Km/hr}}{\frac{1}{2}}=20\text{Km/hr}$