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# Relative velocity

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A motorboat going downstream overcome a raft at a point A; t = 60 min later it turn back and after some time passed the raft at a distance 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant.

https://brainmass.com/physics/relative-velocity/relative-velocity-dimensions-32913

## SOLUTION This solution is FREE courtesy of BrainMass!

Let the speed of the boat in still water be v (constant due to the engine) and flow speed of water is u.
Speed of the boat down the river relative to ground is v + u and the same up the river is v - u.
The raft is flowing with speed of the river i.e. u downstream.
Speed of the boat relative to raft when moving down stream will be (v+u)-u = v and speed of the boat relative to the raft when moving upstream will be
(v - u) + u = v
Therefore in both cases the boat is receding and approaching the raft at the same speed and hence the time taken in both cases is same. Thus the total time elapsed for the two events is 2 x 60 = 120 min.= 2 hour. The distance covered by the boat during this time is 6 km, therefore the speed of the raft i.e. the flow velocity is 6/2 = 3 km/hr.

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