Question

A man is holding an umbrella at an angle of ${30}^{\circ }$ with the vertical with lower end towards himself, which is an appropriate angle to protect him from rain for his horizontal velocity $10m/s$. The speed of the rain is

• A. $10m/s$
• B. $10\sqrt{3}m/s$
• C. $10/\sqrt{3}m/s$
• D. none of these

Answer 1

Answer: (B)

$10\sqrt{3}m/s$

$r=$rain$,g=$ground $\&m=$man
Man can be moving towards either east or west, in both the cases we have, $\overrightarrow{v_{rm}}+\overrightarrow{v_{mg}}=\overrightarrow{v_{rg}}$
$\tan {30}^o=\frac{v_{mg}}{v_{rg}}or{v}_{rg}=v_{mg}\sqrt{3}=10\sqrt{3}m/s$