Question

Rain is falling vertically and a man is moving with velocity $6m{s}^{-1}$. Find the angle at which the man should hold his umbrella avoid getting wet.

Answer 1

${\overrightarrow{v}}_{rain}=-10\hat{j}\Rightarrow {\overrightarrow{v}}_{man}=6\hat{j}$
${\overrightarrow{v}}_{rainw.r.t.man}=-10\hat{j}-6\hat{i}$
$tan\theta =\frac{6}{10}\Rightarrow \theta =ta{n}^{-1}\left(\frac{3}{5}\right)$
where $\theta$ is the angle with vertical.