Question

A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of $2\text{m/s}$. At what angle $\alpha$ with the vertical should the wind screen be placed so that rain drops falling vertically downwards with velocity $6\text{m/s}$ strike the wind screen perpendicularly?

• A. ${\tan }^{-1}\left(\frac{1}{3}\right)$
• B. ${\tan }^{-1}\left(3\right)$
• C. ${\cos }^{-1}\left(3\right)$
• D. ${\sin }^{-1}\left(\frac{1}{3}\right)$

Answer 1

The correct option is B ${\tan }^{-1}\left(3\right)$

Velocity of rain with respect to car ${\overrightarrow{v}}_{RC}={\overrightarrow{v}}_R-{\overrightarrow{v}}_C$ should be perpendicular to the wind screen.
From figure,
$\tan \alpha =\frac{v_R}{v_C}=\frac{6}{2}$
$\alpha ={\tan }^{-1}\left(3\right)$