Question

Rain is falling vertically with a speed of $35\, ms ^{-1}$ . $A$ woman rides a bicycle with a speed of $12 \,ms ^{-1}$ 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
$\vec{v}_{r b}=$ 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