Rain is falling vertically with a speed of 35 m${\mathrm{s}}^{-1}$. Winds starts blowing after sometime with a speed of 12 m${\mathrm{s}}^{-1}$ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

The velocity of the rain and the wind are represented by the vectors $\overrightarrow{{\mathrm{v}}_{\mathrm{r}}} \mathrm{and} \overrightarrow{{\mathrm{v}}_{\mathrm{w}}}$ as shown in the figure. To protect himself from the rain the boy should hold his umbrella in the direction of resultant velocity $\overrightarrow{{\mathrm{v}}_{\mathrm{R}}}$. If $\mathrm{\theta }$ is the angle which resultant velocity $\overrightarrow{{\mathrm{v}}_{\mathrm{R}}}$ makes with the vertical, then tan $\mathrm{\theta }$ = $\frac{{\mathrm{v}}_{\mathrm{w}}}{{\mathrm{v}}_{\mathrm{r}}} = \frac{12}{35} \mathrm{or} \mathrm{\theta } = {\tan }^{-1}\left(\frac{12}{35}\right)$