Question

A man standing on a road has to hold his umbrella at $30°$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\text{km/h}$. He finds that raindrops are hitting his head vertically. What is the speed of rain with respect to the ground?

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

Answer 1

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


Velocity of man, $V_m=10\text{km/h}$
Velocity of rain w.r.t ground $=V_r$
Velocity of rain w.r.t man, $=V_{rm}$
From the velocity triangle,
$V_r\cos {60}^{\circ }=V_m$
$\Rightarrow V_r=\frac{10}{1/2}=20\text{km/h}$