Published by:
CGP EDU Academic Team
Published on: September 12, 2026
If 
is the velocity of a man relative to water, 
is the velocity of water, and 
velocity of man relative to ground, match the following columns, where 
angle between 
and the width of the river.
Column I | Column II | ||
(A) | Minimum distance for | (I) | |
(B) | Minimum time for | (II) | |
(C) | Minimum distance for | (III) | |
(D) | Minimum time for | (IV) |
Text Solution
Verified by ExpertsThe correct answer is:
A
To determine the matching of the columns based on the given information about velocities and angles. Let's analyze:
1. **Column I** describes various scenarios involving a man swimming across a river against a current. The distances and times it takes depend on the relative speeds between the man and the water.
2. **Column II** provides specific conditions for achieving minimum distances and times.
3. Minimum distance is achieved when the man swims directly across the river, so this corresponds to the angle θ being sin inverse of the man's velocity over the water's velocity. Hence, matching A with II makes sense.
4. To minimize time, he must swim diagonally across, corresponding to a different condition. This supports matching B with III.
Given these analyses, we have:
A-II, B-III, C-I, D-IV.
Thus, the answer is Option A.
1. **Column I** describes various scenarios involving a man swimming across a river against a current. The distances and times it takes depend on the relative speeds between the man and the water.
2. **Column II** provides specific conditions for achieving minimum distances and times.
3. Minimum distance is achieved when the man swims directly across the river, so this corresponds to the angle θ being sin inverse of the man's velocity over the water's velocity. Hence, matching A with II makes sense.
4. To minimize time, he must swim diagonally across, corresponding to a different condition. This supports matching B with III.
Given these analyses, we have:
A-II, B-III, C-I, D-IV.
Thus, the answer is Option A.
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