Rain is falling vertically with a speed of (12 ,ms^{-1}). A... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

Rain is falling vertically with a speed of $12 \,ms^{-1}$ . A woman rides a bicycles with a speed of $12 \,ms^{-1}$ in east to west direction. What is the direction in which she should hold her umbrella?

A

$30^\circ$ towards East

B

$45^\circ$ towards East

C

$30^\circ$ towards West

D

$45^\circ$ towards West

Answer

$45^\circ$ towards West

Explanation

Solution

To protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity of the rain with respect to the woman.
$\tan\, \theta= v _{ w } / v _{ f }=12\, m / s$
or, $\tan \,\theta=1$
or, $\theta=45^{\circ}$
Therefore, the direction in which she should hold her umbrella is $45^{\circ}$ toward west.