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  \( {{v}_{0}}=\frac{\ell }{2\tau } \).

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