Question

Rain is falling vertically with a velocity of $25m{s}^{-1}$. A woman rides a bicycle with a speed of $10m{s}^{-1}$ in the north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to safe herself from rain?

• A. $ta{n}^{-1}\left(0.4\right)$
• B. $ta{n}^{-1}\left(1\right)$
• C. $ta{n}^{-1}\left(\sqrt{3}\right)$
• D. $ta{n}^{-1}\left(2.6\right)$

Answer 1

The correct option is A $ta{n}^{-1}\left(0.4\right)$

Here, $v_R=25m{s}^{-1},v_W=10m{s}^{-1}$
Velocity of rain w.r.t. woman : $v_{R/W}=v_R-v_W$
Let $v_{R/W}$ make an angle $\theta$ with vertical, then
$\tan \theta =\frac{v_W}{v_R}=\frac{10}{2.5}=0.4$
She should hold her umbrella at an angle of $\theta ={\tan }^{-1}\left(0.4\right)$ with the vertical towards south.