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Suppose I am solving a question, which has statement written

the velocity of boat in still water 10m/s

Now the question turns to a flowing river, so what will 10m/s be, the relative velocity of the boat wrt the river, or it’s absolute velocity? enter image description here

Here, $V_{sr}$ is relative velocity of boat wrt river and $V_r, V_s$ are velocity of river and boat respectively.

Aditya
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2 Answers2

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Though it's a quite trivial way of questioning in many textbooks, the question should have been more clear.Consider the following question for instance :

Assume there is a boat in which you can manually set boat's velocity vector independent to the flow of the river. If the velocity of boat in still water is $\vec v = 10\hat u$ , where $\hat u$ is a unit vector in some direction and now if the parameters used to set boat's velocity are same but the river's velocity is $\vec r$ ...

We can think of setting boat's velocity independent to that of river's by, say some orthogonally aligned boosters at the top of boat.Though this mechanism of independence will not be specified it is pre-assumed by the question. Now considering $\vec v$ as velocity of boat with respect to the river's velocity $\vec r$ makes sense.

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Relative velocity depends upon frame of reference. It means when you say river is flowing at 10m/s ,it is with respect to a observer who is standing still near the bank, if the frame of reference is that stationary with respect to an observer then relative velocity of boat with respect to river = relative velocity of boat with respect to that observer - relative velocity of river with respect to that observer.