Question

A man is going due west with a velocity of 4 ms${}^{-1}$. It is vertically raining downwards with a velocity of 5 ms${}^{-1}$. At what angle should he hold the umbrella to the vertical so as to protect himself from the rain?

• A. ${\tan }^{-1}\left(\frac{4}{5}\right)$ in anti-clockwise direction
• B. ${\tan }^{-1}(\frac{4}{5})$ in clockwise direction
• C. ${\tan }^{-1}\left(\frac{4}{5}\right)$ North of west
• D. ${\tan }^{-1}\left(\frac{4}{5}\right)$ West of South

Answer 1

The correct option is A ${\tan }^{-1}\left(\frac{4}{5}\right)$ in anti-clockwise direction

$r=$rain$,g=$ground $\&m=$man
We have, $\overrightarrow{v_{rm}}=\overrightarrow{v_{rg}}+\overrightarrow{v_{mg}}$
Resultant $\overrightarrow{v_{rm}}$ makes an angle of $\theta ={\tan }^{-1}\frac{4}{5}$ with vertical. Now this is the direction in which rain falls with respect to man. So, the man must hold his umbrella in opposite direction.
So, man should rotates his umbrella in anti-clockwise direction such that its makes an angle of $\theta ={\tan }^{-1}\frac{4}{5}$ with vertical.