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Question

If vmω = velocity of a man relative to water vω= velocity of water, vm = velocity of man relative to ground, match the following.
Column IColumn IIi. Minimum distance for vmω>vωa.θ=sin1(vmωvω)ii Minimum time for vmωvωb.vmvωiii. Minimum distance for vmω<vωc.vmωvωiv. Minimum time for vmω<vωd.θ=sin1vωvmω

A
i- b,d ii- c iii- a iv- c
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B
i- b,d ii- a iii- a iv- c
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C
i- b,d ii- c iii- a iv- a
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D
i- b,c ii- c iii- a iv- c
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Solution

The correct option is A i- b,d ii- c iii- a iv- c
Distance will be minimum because the man will reach from point A to point B directly.

sinθ=vωvmω and
vmvω
Hence i.b.,d.
Time taken is minimum if vmω is perpendicular to vω.
Hence ii.c.,iv.c.
(ii) If vmω<vω, then drift or distance is shortest if sinθ=vmωvω. Hence (iii)a.

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