Understanding the math in the Michelson-Morley experiment

[aj_17]

[Mentors' note - No template because this post was moved from the Relativity forum]
Summary:: I'm trying to make sense of the trig/algebra in discussing the experiment. This is an excerpt from the textbook Modern Physics (Thornton/Rex) meant to further explain the set up, however I'm not following. Could someone explain this?

If a swimmer (who can swim with speed v2 in still water) wants to swim across a swiftly moving river (speed v1), the swimmer must start heading upriver, so that when the current carries her downstream, she will move directly across the river. Careful reasoning shows that the swimmer’s velocity is sqrt(v2^2-v1^2) throughout her journey (Problem 4).

 

[Nugatory]

The problem is a bit carelessly phrased because it's not respecting the distinction between velocity which is a vector, and speed, which is the magnitude of that vector, and because it's not being clear about which velocities are relative to what.

But with said, you'll be able to get through this problem if you write both the velocity of the water relative to the bank and the velocity of the swimmer relative to the water as vectors with components parallel to and perpendicular to the direction of the water flow. The swimmer's velocity relative to the bank (which is presumably what the problem is lookoing for, although it's not specified) is the sum of these two vectors.

 

[Nugatory]

This thread has been moved into the homework forum. You will have to show your work (there's a big hint in the previoius post) and say where you're getting stuck, and then we can help you over the hard spot