Question

The rain is falling vertically with a speed $4m{s}^{-1}$ and a man is moving due east with a speed $3m{s}^{-1}$. With what speed does the rain appear to be falling (for the man)? Also at what angle should he hold the umbrella to protect himself from rain?

• A. $5m{s}^{-1},{37}^{\circ }\text{with respect to vertical}$
• B. $5m{s}^{-1},{53}^{\circ }\text{with respect to vertical}$
• C. $5m{s}^{-1},{45}^{\circ }\text{with respect to horizontal}$
• D. $5m{s}^{-1},{30}^{\circ }\text{with respect to horizontal}$

Answer 1

The correct option is A $5m{s}^{-1},{37}^{\circ }\text{with respect to vertical}$

The given situation can be shown as


We have from the question
${\overrightarrow{v}}_{rm}=\overrightarrow{v_r}-\overrightarrow{v_m}=-4\hat{j}-3\hat{i}$
$\Rightarrow |\overrightarrow{v_{rm}}|=5m{s}^{-1}$
and $\theta ={\tan }^{-1}\left(\frac{3}{4}\right)={37}^{\circ }$
with respect to vertical.