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Question

If vwm is the velocity of a man relative to water, vw is the velocity of water, and vm is the velocity of man relative to ground, match the following:
Column I
Column II
I.Minimum distance for vmw>vwa.θ=sin1(vmwvw)
II.Minimum time for vmwvwb.vmvw
III.Minimum distance for vmw<vwc.vmwvw
iv.Minimum time for vmw<vwd.θ=sin1vwvmw
where θ is the angle between vmw and the width of the river.

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Solution

i.b,d.;ii.c.;iii.a.;iv.c.
Distance will be minimum because man will reach from A to B directly.
sinθ=vωvmω and vmvω
Hence ib,d
Time taken is minimum if vmω is perpendicular to vω.
Hence ii.c.,ivc.
If vwω<vω, then drift or distance is shortest if
sinθ=vmωvω. Hence (iii)a.
1554561_985388_ans_a9c4ea8cfcae491294a641b380cead63.jpg

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