Question

A cyclist is riding a bicycle with a speed of 35 m/s from north to south. After some time rain starts falling vertically with the same speed as of the cyclist. How the cyclist will hold the umbrella?

• A. 30° with the vertical, towards the south
• B. 45° with the vertical, towards the south
• C. 30° with the vertical, towards the north
• D. 45° with the vertical, towards the north

Hint:

In problems with rain and moving observer, use relative velocity to determine the apparent direction of rain.

Answer 1

The Correct Option is B

Step 1: Concept of relative velocity.
Rain falls vertically relative to ground, but the cyclist's own motion makes it appear slanted.

Step 2: Components of velocity.
Cyclist speed v_c = 35 m/s south; rain speed v_r = 35 m/s vertically downward. Relative velocity of rain w.r.t cyclist: v_rel = v_r - v_c.

Step 3: Computing the angle.
tan θ = v_c / v_r = 35/35 = 1, so θ = 45°. The rain seems to approach from the direction of motion, i.e., towards south.

Step 4: Final inference.
The cyclist should tilt the umbrella 45° from the vertical towards the south.