Question

To a person moving eastwards with a velocity of 4.8 km $h^{-1}$, rain appears to fall vertically down-wards with a speed of 6.4 km $h^{-1}$. Find the actual speed and direction of the rain.

Answer 1

With respect to person the rain make a angle of $\theta$

velocity of person is $v_p=4.8\hat{i}$

velocity of the rain with to man $v_{r/p}=-6.4km{h}^{-1}\hat{j}$

velocity of rain $v_r=v_{r/p}+v_p=4.8km{h}^{-1}\hat{i}-6.4km{h}^{-1}\hat{j}$

speed of the rain $\sqrt{{4.8}^2+{6.4}^2}=8Km{h}^{-1}$

$tan\theta =\frac{6.4}{4.8}=\frac{4}{3}$

$\theta ={53}^0$