Question

A man standing on a road has to hold his umbrella at ${30}^0$ with the vertical to keep the rain away. He throws the umbrella and starts running at 10 $km{h}^{-1}$. He finds that raindrops are hitting his head vertically.
What is the speed of rain with respect to ground?

• A. $10\sqrt{3}km{h}^{-1}$
• B. $20km{h}^{-1}$
• C. $\frac{20}{\sqrt{3}}km{h}^{-1}$
• D. $\frac{10}{\sqrt{3}}km{h}^{-1}$

Answer 1

The correct option is A $10\sqrt{3}km{h}^{-1}$

In vector diagram

$V_r=$ velocity of rain

$V_m=10km/h$ velocity of man

$V_{rm}=$ velocity of rain with respect to man

$V_{rm}=V_r-V_m$

$V_r=V_{rm}+V_m$

By using Lami's theorem,

$\frac{V_m}{sin{30}^0}=\frac{V_{rm}}{sin{60}^0}$

The speed of rain with respect to the ground is,

$V_{rm}=V_m\frac{sin{60}^0}{sin{30}^0}$

$V_{rm}=10\frac{0.8660}{0.5}$

$V_{rm}=10\sqrt{3}=17.32km/h$

The option A is correct.