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 $2m/s$. At what angle $\alpha$ with the vertical should the wind screen be placed so that the rain drops falling vertically downwards with velocity $6m/s$ strike the wind screen perpendicularly?

• A. $ta{n}^{-1}\left(3\right)$
• B. $ta{n}^{-1}\left(4\right)$
• C. $ta{n}^{-1}\left(\frac{1}{3}\right)$
• D. $ta{n}^{-1}\left(\frac{1}{4}\right)$

Answer 1

The correct option is C $ta{n}^{-1}\left(\frac{1}{3}\right)$

We are given that the rain drops falling vertically downwards with velocity $6m/s$ and the car moves horizontally with a velocity $6m/s$. The wind screen is placed on the car as shown. If $\alpha$ is the angle made by the vertical with the wind screen, and the rain falls vertically down,
$tan\alpha =\frac{V_c}{V_r}=\frac{2}{6}=\frac{1}{3}$
Hence, the angle through which the wind screen need to be perpendicular to the rain is $\alpha =ta{n}^{-1}\frac{1}{3}$ or $\alpha =ta{n}^{-1}\frac{1}{3}$