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 m/s. At what angle $\alpha$ with the vertical should the screen be placed so that the rain drops falling downwards with velocity 6 m/s strike the windscreen 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. i.e. net components of $\overrightarrow{v_R}$

$tan\alpha =\frac{V_C}{V_R}=\frac{2}{6}=1/3\alpha =ta{n}^{-1}\left(1/3\right)$