A man is walking with $3 \mathrm{m}/\mathrm{s}$, due east. Rain is falling vertically downwards with speed $4 \mathrm{m}/\mathrm{s}$. Find the direction in which man should hold his umbrella, so that rain does not wet him.

He should hold his umbrella in the direction of $v_{rm} or v_r-v_m$. 

$$\begin{gathered} 0\mathrm{P}={\mathrm{v}}_r+\left(-{\mathrm{v}}_m\right)={\mathrm{v}}_{\mathrm{r}}-{\mathrm{v}}_{\mathrm{m}}={\mathrm{v}}_{\mathrm{rm}} \\ \mathrm{tan\theta }=\frac{3}{4} \\ \mathrm{\theta }={\tan }^{-1}\left(\frac{3}{4}\right)=37° \end{gathered}$$

Therefore, man should hold his umbrella at an angle of ${37}^o$ east of vertical ( or  ${37}^o$ from vertical towards east)