Question

A man is going due east with a velocity of $5m/s$. It is vertically raining downwards with a velocity of $4m/s$. At what angle should he hold the umbrella to the vertical so as to protect himself from the rain?

• A. ${\tan }^{-1}\left(\frac{5}{4}\right)$ in anticlockwise direction.
• B. ${\tan }^{-1}\left(\frac{5}{4}\right)$ in clockwise direction.
• C. ${\tan }^{-1}\left(\frac{4}{5}\right)$ in anticlockwise direction.
• D. ${\tan }^{-1}\left(\frac{4}{5}\right)$ in clockwise direction.

Answer 1

Answer: (B)

${\tan }^{-1}\left(\frac{5}{4}\right)$ in clockwise direction.

Relative to man, rain is coming from east at $5km/h$ and from top at $4km/h$.
Hence, from vertical, the angle is ${\tan }^{-1}\left(5/4\right)$ in clock-wise direction.