Question

Rain is falling vertically with a speed of 30 m/s. A woman rides a bicycle with a speed of 10 m/s in the north to south direction. What is the direction in which she should hold her umbrella then?

Answer 1

Here,

$v_c=$Velocity of the cyclist

$v_r=$Velocity of falling rain

In order to protect herself from the rain, the women must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the women

$v=v_r+(-v_c)$

$v=30+(-10)=20m/s$

$\tan \theta =\frac{v_c}{v_r}=\frac{10}{30}$

$\theta ={\tan }^{-1}\left(\frac{1}{3}\right)$

$\theta \approx 18°$

Hence the women must hold the umbrella towards the south, at angle of nearly 18° with the vertical