Question

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

Answer 1

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.