A man is running with velocity 5km/h towards east and rain is falling vertically down with speed 5km/h. Direction of rain w.r.t man is-

(a) 30 degree with vertical

(b) 60 degree with vertical

(c) 45 degree with vertical

(d) 90 degree with vertical

From above diagram we can see direction of rain is downward and man is moving towrds east direction, so speed of rain with respect to man, $v_{rm}=v_r\hat{j}-v_m\hat{i}$

Speed of man, $v_m={5ms}^{-1}$

Speed of rain, $v_r=5m{s}^{-1}$

So,

$tan\theta =\frac{v_m}{v_r}=\frac{5{ms}^{-1}}{5m{s}^{-1}}=1$

$\theta ={tan}^{-1}1⟹\theta ={45}^o$

So, Direction of rain w.r.t man is; 45 degree with vertical.