Question

A car with a vertical windshield moves in a rainstorm at a speed of $ 40km/hr $ . The raindrops fall vertically with a constant speed of $ 20m/s $ . The angle at which raindrops strike the windshield is:
A. $ {\tan ^{ - 1}}\dfrac{5}{9} $
B. $ {\tan ^{ - 1}}\dfrac{9}{5} $
C. $ {\tan ^{ - 1}}\dfrac{3}{2} $
D. $ {\tan ^{ - 1}}\dfrac{2}{3} $

Answer 1

Hint: To solve this question, first we will convert the speed of a car into $ m/s $ and then we have both the speed of a car and the speed of the raindrops which are vertically falling. Now, we can find the angle at which raindrops strike the windshield of the car.

Complete step by step solution:
The horizontal component of falling rain is $ 40km/hr $ .
Convert $ km/hr $ into $ m/s $ :
 $ 40km/hr = 40 \times \dfrac{5}{{18}}m/s = \dfrac{{200}}{{18}}m/s $
And, the vertical component of falling rain is $ 20m/s $
Now, the angle at which raindrops strike the windshield is:
 $
  Q = {\tan ^{ - 1}}(\dfrac{{horizontal}}{{vertical}}) \\
   \Rightarrow Q = {\tan ^{ - 1}}(\dfrac{{\dfrac{{200}}{{18}}}}{{20}}) \\
  \therefore Q = {\tan ^{ - 1}}(\dfrac{5}{9}) \\
  $
Therefore, the angle at which raindrops strike the windshield is $ {\tan ^{ - 1}}\dfrac{5}{9} $ .
Hence, the correct option is (A.) $ {\tan ^{ - 1}}\dfrac{5}{9} $ .

Note:
When you are in a moving car the raindrop appears to be moving towards you, but that is actually because you are moving towards it, in the same way that trees appear to be moving in the opposite direction to you if you look out of the side window.