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)

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