Rain is falling vertically with a speed of $35 ext{ m/s}$. Wind starts blowing after sometime with

Question

Rain is falling vertically with a speed of $35	ext{ m/s}$. Wind starts blowing after sometime with a speed of $12	ext{ m/s}$ in the east to west direction. At what angle to the vertical should a boy waiting at a bus stop hold his umbrella?

Professor PC Thomas Classes · Answer

The velocity of rain is downward and wind is east to west. The resultant velocity of the rain is $\vec{R} = \vec{v}_r + \vec{v}_w$. The direction $	heta$ that $\vec{R}$ makes with the vertical is $	an	heta = \frac{v_w}{v_r} = \frac{12}{35} = 0.343$. Since the rain is blown towards the west, the boy must hold his umbrella towards the east to oppose it.