A swimmer is capable of swimming 0.60 m/s in still water.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. This swimmer directs herself directly across the river at 0.6 meters per second; the river goes downstream at 0.5 meters per second and the river is 0.5 meters wide and the question is how far downstream will she reach the other side of the river? So she's gonna be going somewhat in this direction that's gonna be her resultant velocity and so she's not gonna actually reach this point in the opposite side that she's aiming for initially instead she will end up somewhere down here; so what is that distance? And then the next question is, how long does it take her to get across? But the easier question to answer first is the time; we know the y-component of her velocity we'll call this d y and it equals v y times t and we know v y because the y-component of this resultant velocity is her velocity the swimmer with respect to the water because the water with respect to the river bank has no y-component. We'll find t by dividing both sides by v y and so the time is this y-displacement divided by the y-component of the velocity. So that's 45 meters divided by 0.6 meters per second which is 75 seconds and then we can use that in part (a) to figure out how far downstream she will reach the opposite shore because we know how long she spends swimming—75 seconds— and we know the x-component of her velocity as well which is entirely due to the water with respect to the river bank which is 0.5 meters downstream, meters per second. So the x-displacement then is v x times t and that's the velocity of the water with respect to the shore— I guess I called it up bank up there didn't I so put a B there— times time. So that's 0.5 meters per second times 75 seconds and that gives 38 meters downstream will be this distance here where she will reach the river bank 38 meters downstream from where she originally intended.