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Question

# A swimmer crosses a river of width d flowing at velocity v. While swimming he heads himself always at an angle of 120o with the river flow and on reaching to the other end he finds a drift of d/2 in the direction of flow of river. The speed of swimmer with respect to the river is -

A
(23)v
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B
2(23)v
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C
4(23)v
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D
(2+3)v
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Solution

## The correct option is C 4(2−√3)vIn the given figureAB=d2VR=√(Vm)2+V2+2VmVcos120so,VR=√Vm2+V2−VmV.........(1)Let θ be the angle made by the resultant velocity vector with the flow of the river from parallelogram law of vector addition.θ=Vmsin120V+Vmcos120..........(2)In ΔABC, ∠AOB=(90−θ)tan(90−θ)=d/2d=12cotθ=12soθ=tan−12.........(3)tan−12=Vmsin120V+Vmcos120from (2) and (3)03.43=Vm×(0.86)V−0.5vVm=1.95vputting this in (1) we get VR=√(1.91v)2+v2−1.95v2Hence,Option C is correct answer.

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