Question

Rain is falling vertically with a speed of $20m/s$ . After sometime wind starts blowing with a speed of $12m/s$ in east to west direction in which direction should a boy waiting at a bus stop hold his umbrella.

Answer 1

The direction of the resultant velocity vector with the vertical is given as,

$\theta ={\tan }^{-1}\left(\frac{v_w}{v_r}\right)$

$\theta ={\tan }^{-1}\left(\frac{12}{20}\right)$

$={30.96}^{\circ }$

Thus, the direction of umbrella should be towards east making an angle of ${30.96}^{\circ }$ with the vertical.