What does speed of an object relative to water mean?

Question

A swimmer swims with the velocity 1.25 m/s "relative to water". He has to swim across the river which is 150 meters wide. If his direction of velocity is perpendicular to the stream, he is taken away by the stream 120 meters below. What direction relative to the stream does he have to choose in order to get to the opposite point on the other side? How long will it take him?

My question is what does "relative to water mean"? I am not sure how to imagine it when the water is moving.

Edit: Is my interpretation of velocity (relative to something) in these images correct? If not, can you please draw an image where the "velocity of the swimmer relative to water" would be shown? Or at least how do I find out?

Metersquared · Answer

That's actually a great question, which brings you to the need of material derivatives in fluid dynamics, since flow velocity will not only be time dependent, but also position dependent.

Now for the actual question. I believe, it assumes that the flow velocity is homogeneous (the same in every point). With this in mind, it becomes a simple relative velocity problem to solve. For your interpretation for relative velocity, the one for the relative velocity to the ground is correct, but I believe the latter isn't. You could imagine the stream is actually the water, and it's carrying the swimmer with it, hence the relative velocity of the swimmer to the water is also just its relative velocity to the stream.

What does speed of an object relative to water mean?

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