Question

It is raining vertically with a velocity of $25{\text{ms}}^{-1}$. A woman rides a bicycle with a speed of $10{\text{ms}}^{-1}$ in north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to save herself from the rain?

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

Answer 1

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

Here, $v_R=25{\text{ms}}^{-1},v_W=10{\text{ms}}^{-1}$
$\therefore$ Velocity of rain w.r.t woman, $\overrightarrow{v_{RW}}=\overrightarrow{v_R}-\overrightarrow{v_W}$
Let $\overrightarrow{v_{RW}}$ makes an angle $\theta$ with vertical then,
$\tan \theta =\frac{v_W}{v_R}=\frac{10}{25}=0.4$


She should hold her umbrella at an angle of $\theta ={\tan }^{-1}\left(0.4\right)$ with vertical.