Question

Rain is falling vertically with a speed of $30m{s}^{-1}$. A woman rides a bicycle with a speed of $10m{s}^{-1}$ in the north to south direction. What is the direction in which she should hold her umbrella ?

Answer 1

The described situation is shown in the given figure.
Here, $v_c$= Velocity of the cyclist
$v_r$ = Velocity of falling rain
In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity $\left(v\right)$ of the rain with respect to the woman.

$tan\theta =v_c/v_r=10/30$

$\theta ={18}^o$

Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18 with the vertical.