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Question

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 20 min. The velocity of the river water in km/hr is

A
1
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B
3
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C
4
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D
4.5
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Solution

The correct option is C 4
Let Vr be the magnitude of velocity of river and Vb be the magnitude of velocity of boat in still water.
Displacement = 1 km
t=2060=13 hr

Velocity along AB=ABt
Vbcos(θ)=113=3 km/hr
From velocity triangle ABC,
V2b=V2r+(Vbcosθ)2
V2r=V2b(Vbcosθ)2
V2r=5232=16
Vr=4 km/hr

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