Rain drops fall vertically at a speed of $20 \mathrm{m }{\mathrm{s}}^{-1}$. At what angle (in degree) do they fall on the wind screen of a car moving with a velocity $15 \mathrm{m }{\mathrm{s}}^{-1}$, if the wind screen is inclined at an angle of $23°$ to the vertical? [${\tan }^{-1}\left(0.75\right)\approx 37°$]

Solution

$\tan (90°-\theta )=\frac{20}{15}$

$\therefore \mathrm{c}\mathrm{o}\mathrm{t}\theta =\frac{20}{15}=\frac{4}{3}$

$\Rightarrow \theta =37°$

$\therefore \varphi =37°+23°=60°$ (Angle made with the windscreen)

Hence, the correct answer is 60.