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 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?
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In problems with rain and moving observer, use relative velocity to determine the apparent direction of rain.
Updated On: Jun 19, 2026
- 30° with the vertical, towards the south
- 45° with the vertical, towards the south
- 30° with the vertical, towards the north
- 45° with the vertical, towards the north
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The Correct Option is B
Solution and Explanation
Step 1: Understanding relative motion.
The rain appears vertical to an observer on the ground but due to cyclist's motion, the rain appears slanted to the cyclist.
Step 2: Velocity components.
- Cyclist velocity: \(v_c = 35~\text{m/s}\) south
- Rain velocity: \(v_r = 35~\text{m/s}\) vertically down
- Relative velocity of rain with respect to cyclist: \(\vec{v}_{rel} = \vec{v}_r - \vec{v}_c\)
Step 3: Angle calculation.
\[ \tan \theta = \frac{v_c}{v_r} = \frac{35}{35} = 1 \implies \theta = 45^\circ \] The rain will appear to come at 45° to the vertical in the direction opposite to cyclist motion (towards south).
Step 4: Conclusion.
Cyclist should hold the umbrella at 45° with the vertical, towards the south.
The rain appears vertical to an observer on the ground but due to cyclist's motion, the rain appears slanted to the cyclist.
Step 2: Velocity components.
- Cyclist velocity: \(v_c = 35~\text{m/s}\) south
- Rain velocity: \(v_r = 35~\text{m/s}\) vertically down
- Relative velocity of rain with respect to cyclist: \(\vec{v}_{rel} = \vec{v}_r - \vec{v}_c\)
Step 3: Angle calculation.
\[ \tan \theta = \frac{v_c}{v_r} = \frac{35}{35} = 1 \implies \theta = 45^\circ \] The rain will appear to come at 45° to the vertical in the direction opposite to cyclist motion (towards south).
Step 4: Conclusion.
Cyclist should hold the umbrella at 45° with the vertical, towards the south.
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