Question

When it is raining vertically down, to a man walking on road the velocity of rain appears to be $1.5$ times his velocity. To protect himself from rain he should hold the umbrella at an angle $\theta$ to vertical. Than $\tan \theta =$

• A. $\frac{2}{\sqrt{5}}$
• B. $\frac{\sqrt{5}}{2}$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{2}{\sqrt{5}}$

$\sin \theta =\frac{|\overrightarrow{V}m,g|}{|\overrightarrow{V}r,m|}=\frac{x}{1.5x}$

$\therefore \sin \theta =\frac{2}{3}\therefore \theta ={\sin }^{-1}\left(\frac{2}{3}\right)$

$\therefore \tan \theta =\frac{2}{\sqrt{5}}$