Question

Rain is falling vertically with speed of 35 m/s. A woman rides a bicycle with a speed of 15 m/s in East to West direction. What is the direction in which she should hold her umbrella?

• A. $\tan ^{-1}\left(\frac{3}{7}\right)$ with the vertical towards west
• B. $\tan ^{-1}\left(\frac{4}{7}\right)$ with the vertical towards east
• C. $\tan ^{-1}\left(\frac{5}{7}\right)$ with the vertical towards east
• D. Towards North downward

Answer 1

Answer: (A)

$\overrightarrow{ V }_{ r }=35 m / s$
$\overrightarrow{ V }_{ b }=15 m / s$
$\tan \theta=\frac{ AD }{ OA }$
$\Rightarrow \tan \theta=\frac{\overrightarrow{ V _{ b }}}{\overrightarrow{ V }_{ r }}$
$=\frac{15}{35}=\frac{3}{7}=0.4285$
$\theta=\tan ^{-1}(0.4285)=23.19^{0}$