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 1

Answer: (D)

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.