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Question

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point ‘C’ starting from ‘A’. He swims with a speed of 5 km/hr at an angle θ w.r.t the river flow. If AB =BC =400 m, what is the value of θ?


A

37

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B

53

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C

30

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D

60

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Solution

The correct option is B

53


Resultant path of the swimmer is at 45 with the bank. Therefore x and y-components of swimmer’s resultant velocity must be equal.
tan 45=vyvxvy=vxvR+vm cos θ=vm sin θ1+5 cos θ=5 sin θ
Squaring both sides, 1+25cos2θ+10cosθ=2525cos2θ50 cos2 θ+10 cos θ24=0
Solving, we get θ=53.


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