Rain is falling vertically downward with velocity 4 m/s. A man is moving horizontally with velocity 3 m/s, the velocity of rain with respect to man is

Relative velocity of man w.r.t. ground

v_mg = 3 m/s

          Relative velocity of rain w.r.t. ground,

          v_mg = 3 m/s

Relative velocity of rain. W.r.t. man, v_rm = ?

         ${\mathbf{v}}_{rm}={\mathbf{v}}_{rg}-{\mathbf{v}}_{mg}={\mathbf{v}}_{rg}+\left(-{\mathbf{v}}_{mg}\right)$

       $v_{rm} = 5 m/s$

       $\tan \alpha =\frac{3}{4}, \tan \beta =\frac{4}{3}$

${\mathbf{v}}_{rm}=5 \mathrm{m}/\mathrm{s}\text{ at }{\tan }^{-1}\left(\frac{3}{4}\right)$ with vertical or at ${\tan }^{-1}\left(\frac{4}{3}\right)$ with horizontal.