Question:
A man rides a bicycle with a speed of \( 17.32 \text{ m s}^{-1} \) in east-west direction. If the rain falls vertically with a speed of \( 10 \text{ m s}^{-1} \), the direction in which he must hold his umbrella is
A man rides a bicycle with a speed of \( 17.32 \text{ m s}^{-1} \) in east-west direction. If the rain falls vertically with a speed of \( 10 \text{ m s}^{-1} \), the direction in which he must hold his umbrella is
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Always use relative velocity when observer is moving.
Updated On: May 2, 2026
- $30^\circ$ with the vertical towards east
- $60^\circ$ with the vertical towards west
- $30^\circ$ with the vertical towards west
- $60^\circ$ with the vertical towards east
- $0^\circ$ with the vertical
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The Correct Option is B
Solution and Explanation
Concept: Relative velocity of rain w.r.t. man
To avoid rain, umbrella must be aligned opposite to apparent velocity of rain. ---
Step 1: Given velocities
• Velocity of rain (vertical downward): \[ \vec{v}_r = 10 \text{ m/s} \]
• Velocity of man (horizontal east): \[ \vec{v}_m = 17.32 \text{ m/s} \] ---
Step 2: Relative velocity of rain w.r.t man
\[ \vec{v}_{rm} = \vec{v}_r - \vec{v}_m \] Components:
• Horizontal = $-17.32$ (west direction)
• Vertical = $10$ (downward) ---
Step 3: Find angle
\[ \tan \theta = \frac{\text{horizontal}}{\text{vertical}} = \frac{17.32}{10} \] \[ \tan \theta = 1.732 \] \[ \theta = 60^\circ \] ---
Step 4: Direction
• Rain appears coming from front (west side)
• So umbrella tilted towards west --- Final Answer: \[ \boxed{60^\circ \text{ with vertical towards west}} \]
To avoid rain, umbrella must be aligned opposite to apparent velocity of rain. ---
Step 1: Given velocities
• Velocity of rain (vertical downward): \[ \vec{v}_r = 10 \text{ m/s} \]
• Velocity of man (horizontal east): \[ \vec{v}_m = 17.32 \text{ m/s} \] ---
Step 2: Relative velocity of rain w.r.t man
\[ \vec{v}_{rm} = \vec{v}_r - \vec{v}_m \] Components:
• Horizontal = $-17.32$ (west direction)
• Vertical = $10$ (downward) ---
Step 3: Find angle
\[ \tan \theta = \frac{\text{horizontal}}{\text{vertical}} = \frac{17.32}{10} \] \[ \tan \theta = 1.732 \] \[ \theta = 60^\circ \] ---
Step 4: Direction
• Rain appears coming from front (west side)
• So umbrella tilted towards west --- Final Answer: \[ \boxed{60^\circ \text{ with vertical towards west}} \]
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