A motorboat going downstream overcame a raft at a point A;  $$\tau =60\,\,\min$$  later it turned back and after some time passed the raft at a distance  $$\ell =6.0\,\,km$$from the point Find the flow velocity assuming the duty of the engine to be constant.

Solution:

Let v0 be the stream velocity and  $${v}’$$ the velocity of motorboat with respect to water. The motorboat reached point B while going downstream with velocity  $$({{v}_{0}}+{v}’)$$ and then returned with velocity  $$({v}’-{{v}_{0}})$$ and passed the raft at point C. Let t be the time for the raft (which flows with stream with velocity v0) to move from point A to C, during which the motorboat moves from A to B then from B to C.

Therefore

$$\frac{\ell }{{{v}_{0}}}=\tau +\frac{({{v}_{0}}+{v}’)\tau -\ell }{({v}’-{{v}_{0}})}$$.

On solving we get  $${{v}_{0}}=\frac{\ell }{2\tau }$$.

## Kinematics!

#### A motorboat going downstream overcame a raft at a point A; τ=60min later it turned back and after some time passed the raft at a distance ℓ=6.0kmfrom the point Find the flow velocity assuming the duty of the engine to be constant

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