Physics · MOTION IN A PLANE

A man standing on a road observes rain falling vertically at a speed of \( 20\text{ m/s} \). When he starts running horizontally at \( 20\text{ m/s} \), the rain appears to hit him at an angle \( \theta_1 \) with the vertical. If he doubles his running speed to \( 40\text{ m/s} \), the rain appears to hit him at an angle \( \theta_2 \) with the vertical. Calculate the ratio \( \frac{\tan\theta_2}{\tan\theta_1} \).

1. A
   \( 1/2 \)
2. B
   1
3. C
   2
4. D
   \( \sqrt{2} \)