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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