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Question

A man swims from a point A on one bank of a river of width 100 m . When he swims perpendicular to the water current, he reaches the other bank 50 m downstream. The angle to the bank at which he should swim, to reach the directly opposite point B on the other bank is

A
80 with the direction of flow of river
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B
110 with the direction of flow of river
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C
120 with the direction of flow of river
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D
150 with the direction of flow of river
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Solution

The correct option is C 120 with the direction of flow of river
Let vmw be the velocity of man w.r.t river and vw be the velocity of river.

From figure (a), we get
tanθ=vwvmw=50100=12
or vmw=2vw
Using Figure (b), we can say
sinα=vwvmw=vw2vw=12
or α=30
Angle with the direction of flow, α+90=120
So, it is 120 with the direction of flow of river

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