A boat is sent across a river with a velocity of 3km/h. If the resultant velocity of the boat is 5km/h, then velocity of the river flow is
A
8km/h
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B
10km/h
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C
6km/h
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D
4km/h
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Solution
The correct option is D4km/h From the relation we have −→vb,r=→vb−→vr...(i) given that velocity of boat w.r.t river is −→vb,r=3km/h^j Let the direction of river flow is along +vex axis, hence velocity of river w.r.t ground is vrkm/h^i
⇒ The velocity of boat w.r.t ground is →vb=−→vb,r+→vr →vb=3^j+vr^i Hence resultant speed, |→vb|=√32+v2r, given that |→vb|=5km/h ⇒52=32+v2r ⇒v2r=25−9=16 ∴vr=√16=4km/h