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

• Correct answer
  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

Solution

Given, speed of rain in vertical direction, $v_r=30 \mathrm{~m} / \mathrm{s}$
The given situation is shown in the above figure. If $\theta$ be the angle from vertical in south direction, then, $\tan \theta=\frac{v_m}{v_r}=\frac{10}{30}=\frac{1}{3}$ $\therefore \quad \theta=\tan ^{-1}\left(\frac{1}{3}\right)$ towards West direction.

Hence, the correct answer is option: 'A'.