A boat which has a speed 5km/h in still water crosses a river 100m wide along the shortest possible path in 1.5 minutes, the velocity of river water in km/h is
A
3.0
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B
3
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C
3.00
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Solution
The shortest path that the boat could cross is OB. For this, the boat will have to move against the direction of flow of river at some angle.
Assuming origin at point O, rightward direction be positive x− axis and OB be positive y− axis. Let velocity of the river be, →vr=v^i and velocity of boat w.r.t. the ground be →vb.
Given that velocity of the boat w.r.t. river, ∣∣→vbr∣∣=5km/h
Now, width of the river, OB=100m=0.1km
Time taken by the boat to cross the river, t=1.5min=1.560h ∴∣∣→vb∣∣=OBt=0.1km1.560h=6015=4km/h ⇒→vb=4^jkm/h
Velocity of boat w.r.t. river, −→vbr=→vb−→vr →vbr=4^j−v^i ∣∣→vbr∣∣=5=√42+v2 v=√25−16=3km/h ∴ Velocity of river =3km/h