Question

A car with vertical windshield moves in a rainstorm at a speed of $40km/hr$. The rain drops fall vertically with a constant speed of $20m/s$. The angle at which raindrops strike the windshield is:

Answer 1

Step 1: Given

Speed of the car, $v_c=40km/hr=\frac{100}{9}m/s$

Speed of the raindrop, $v_r=20m/s$

Step 2: Draw the free body diagram

Step 3: Determine the angle

The resultant angle is given by,

$$\begin{gathered} \tan \theta =\frac{v_c}{v_r} \\ =\frac{{\displaystyle \frac{100}{9}}}{20} \\ \tan \theta =\frac{5}{9} \\ \Rightarrow \theta ={\tan }^{-1}\frac{5}{9} \end{gathered}$$

Therefore, the raindrop will strike the windshield at an angle of ${\tan }^{-1}\frac{5}{9}$.