Question

A man rides a bicycle with a speed of $17.32$ $m{s}^{-1}$ East-West direction. If the rain falls vertically with a speed of $10$ $m{s}^{-1}$, then the direction in which he must hold his umbrella is:

• A. ${30}^o$ with the vertical towards East
• B. ${60}^o$ with the vertical towards West
• C. ${30}^o$ with the vertical towards West
• D. ${60}^o$ with the vertical towards East
• E. $0^o$ with the vertical

Answer 1

The correct option is B ${60}^o$ with the vertical towards West

Speed of bicycle$=17.32m{s}^{-1}$
Speed of rain$=10m{s}^{-1}$
From figure
$\tan \theta =\frac{V_M}{V_R}=\frac{17.32}{10}=1.732=\sqrt{3}=\tan \theta {60}^o$
$\Rightarrow \tan \theta ={60}^o$
or $\theta ={60}^o$ with vertical towards West.