Question

Rain is falling vertically with a speed of $35m{s}^{-1}$ . $A$ woman rides a bicycle with a speed of $12m{s}^{-1}$ in east to west direction. The direction in which she should hold her umbrella is

• A. $\theta ={\tan }^{-1}\left(\frac{12}{35}\right)$ with vertical towards the east
• B. $\theta ={\tan }^{-1}\left(\frac{12}{35}\right)$ with vertical towards the west
• C. $\theta ={\tan }^{-1}\left(\frac{12}{37}\right)$ with vertical towards the north
• D. $\theta ={\tan }^{-1}\left(\frac{12}{37}\right)$ with vertical towards the south

Answer 1

Answer: (B)

${\vec{v}}_b=$ Velocity of bicycle
${\vec{v}}_r=$ velocity of rain
${\vec{v}}_{rb}=$ velocity of rain w.r.t bicycle
$\tan \theta =\frac{v_b}{v_r}=\frac{12}{35}$
Therefore, the woman should hold her umbrella at an angle of $\theta ={\tan }^{-1}\left(\frac{12}{35}\right)$ with the vertical towards west