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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 away from point B downstream. The angle to the bank at which he should swim, to reach the directly opposite point B on the other bank is (in both the cases speed of man with respect to river is same)

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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.

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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