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Question

A boat goes across a river in shortest possible time with a velocity 12 km/h . The magnitude of its resultant speed in flowing water is 13 km/h. The magnitude of velocity of water flow in the river is

A
5 km/h
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B
7 km/h
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C
9 km/h
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D
1 km/h
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Solution

The correct option is A 5 km/h
Let Vbr be the velocity of boat w.r.t river and Vr be the velocity of water flow in river.
According to question,
Vbr=12 km/h (Vbr is perpendicular to the flow of the river for shortest time)
and
Velocity of boat w.r.t ground, Vb=13 km/h
We know that
Vbr=VbVrVb=Vbr+VrVb=V2br+V2r
Vb=122+V2r
13=144+V2r
V2r=25Vr=5 km/h

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