Question

Rain is falling vertically with a speed of $30\, m / s .$ A man rides a bicycle with a speed of $10\, m / s$ from East to West direction. At what the angle with the vertical, he sees the rain falling?

• A. $\tan ^{-1}\left(\frac{1}{3}\right)$ towards West
• B. $\tan ^{-1}(3)$ towards West
• C. $\tan ^{-1}\left(\frac{1}{3}\right)$ towards East
• D. $\tan ^{-1}(3)$ towards East

Answer 1

Answer: (A)

Given, speed of rain in vertical direction,
$v_{r}=30\, m / s$
Speed of man, $v_{m}=10\, m / s$ from direction East to West

The given situation is shown in the above figure. If $\theta$ be the angle from vertical in south direction, then,
$\tan \,\theta=\frac{v_{m}}{v_{r}}=\frac{10}{30}=\frac{1}{3}$
$\therefore \theta=\tan ^{-1}\left(\frac{1}{3}\right)$ towards West direction.