[jaysay21]

A swimmer is capable of swimming 0.50 m/s in still water.
If she aims her body directly across a 75 m-wide river whose current is 0.35 m/s, how far downstream (from a point opposite her starting point) will she land?

[FlyYakker]

Given a velocity, what do you need to calculate a distance?

[Unknown008]

Here, you need to draw a diagram of forces. Say your river is flowing from west to east, and your swimmer is crossing northwards. There is a forward force of 0.50m/s (note that it is not a force, but it eases the work) and a side force towards the east, of 0.35m/s.

Now calculate the time to reach the other end of the river without the current. Then use that answer to calculate the distance moved by the water during that time. This distance is the answer.

[FlyYakker]

As Unknown008 says, speed is not a force so don't get the terms confused. Speed in a specific direction is a vector quantity so it is perfectly OK to draw the swimmer and water speeds in this case as vectors if you need to do so to as a part of the problem, or to simply help you visualize it. My hint was to simply figure the time to directly across, which as noted, gives the time for the moving water to deflect the swimmer downstream, from which you may derive the distance downstream.