Question

Rain is falling vertically with a speed of \( 36\ \mathrm{m/s} \) and a boy is moving on a bicycle with a speed of \( 20\ \mathrm{m/s} \) towards south. The angle with the vertical towards south with which the boy has to hold an umbrella is

• A. \( \tan^{-1}\left( \dfrac{5}{9} \right) \)
• B. \( \sin^{-1}\left( \dfrac{5}{9} \right) \)
• C. \( \cos^{-1}\left( \dfrac{5}{9} \right) \)
• D. \( \cot^{-1}\left( \dfrac{5}{9} \right) \)

Hint:

Always consider the relative motion of rain with respect to the observer to determine the angle for the umbrella.

Answer 1

The Correct Option is A

Relative motion of rain with respect to boy: Vertical = 36 m/s, Horizontal = 20 m/s
So, \( \theta = \tan^{-1}\left(\dfrac{20}{36}\right) = \tan^{-1}\left(\dfrac{5}{9}\right) \)