Question

Rain is falling vertically with a speed of $35m{s}^{-1}$. A women rides bicycle with a speed of $12m{s}^{-1}$ in east to west direction. In which direction should she hold her umbrella?

Answer 1

She should hold the umbrella a little inclined towards the west from the vertical.

The drops which are falling a little ahead of the current position of the woman, will fall on her, because she moves in that direction.

relative velocity of the rain drops wrt cyclist = velocity of woman - velocity of rain

the magnitude of relative velocity the rain drops wrt woman = $\sqrt{\left({12}^2+{35}^2\right)}=37m/s$

direction . relative velocity of the rain drops = ${\tan }^{-1}\left(12/35\right)=18.92deg$ from the vertical.

So the cyclist should hold the umbrella at $18.92deg$ to the vertical in the forward direction.