Question

Rain is falling vertically with a speed of $35$ $m{s}^{-1}$. Winds starts blowing after sometime with a speed of $12$ $m{s}^{-1}$ in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella?

Answer 1

The resultant velocity of raindrops will be the vector sum of the raindrop speed (vertical) and the horizontal wind speed.

the magnitude of the result velocity of the rain drops =$\sqrt{{12}^2+{35}^2}=37m/sec$

the direction of the resultant velocity vector with the vertical $=tan⁻¹\frac{12}{35}={18.92}^o.$

The umbrella should be pointed in the direction opposite to the resultant velocity of the raindrops. So it should be in the direction ${18.92}^0$. inclination to the vertical opposite to the direction of wind., towards East.

or, ${71.08}^0$. with the horizontal (East) towards the vertical.