A boat which has a speed of 5km/hr in still water crosses a river of width 1km along the shortest possible path in 20min. 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 C4 Let Vr be the magnitude of velocity of river and Vb be the magnitude of velocity of boat in still water. Displacement = 1km t=2060=13hr
Velocity along AB=ABt Vbcos(θ)=113=3km/hr From velocity triangle ABC, V2b=V2r+(Vbcosθ)2 ⇒V2r=V2b−(Vbcosθ)2 ⇒V2r=52−32=16 ⇒Vr=4km/hr