Suppose that you are swimming in a river while a friend watches from the shore. In calm water, you swim at a speed of 1.25 m/s . The river has a current that runs at a speed of 1.00 m/s . Which of the following gives the correct components for the current velocity and the pure swimming velocity (i. e., the velocity that you would have in still water) using this coordinate system?

Explanation:

Given that

If you swim at speed in calm water 1.25m/s

Current speed of the water is 1m/s

Let assume you are swimming in positive x-axis, then, Va=1.25 m/s

Then, let assume the river is flowing in the opposite direction, then it will be negative x axis Vr=-1m/s

If you are swimming against the current in a river, then the river is slowing you down.

Therefore, your speed would be

V=Va+Vr

V=1.25•im/s−1.00•im/s = 0.25•im/s

Then, if you moving in the direction of the current the speed will be faster, this is just like when a car is driving down a slope road,

Now if the river and the you are in the same direction, let assume positive x axis

Then, Va=1.25 •i m/s

Vr=1.00 •im/s

Then, V=Va+Vr

v = 1.25•i+ 1•i=2.25 •im/s