# Basic Relativity Question

1. Feb 15, 2012

### Crazysah

1. The problem statement, all variables and given/known data

The Michelson-Morley experiment for a real wind (This is taken from Resnick and Halliday, Basic Concepts in Relativity (MacMillan, New York, 1992).
A pilot plans to fly due east from A to B and back again. If u is her airspeed (speed of plane with respect to the air) and if l is the distance between A and B, it is clear that her roundtrip time t — if there is no wind — will be 2l/u.
a) Suppose, however, that a steady wind of speed v blows from the west. What will the round trip travel time now be, expressed in terms of l, u, and v?
b) If the wind is from the south, explain how you would find the expected roundtrip travel time, again as a function of l, u, and v. (If you can find the travel time, do it!)
c) Note that these two travel times are not equal. Should they be? Did you make a mistake?
d) In the Michelson-Morley experiment, however, the experiment seems to show that (for arms of equal length) the travel times (and thus path lengths) for light are equal; otherwise these experimenters would have found a pattern shift when they rotated their experiment. What is the essential difference between these two situations?

2. Relevant equations

Distance = speed x time.

3. The attempt at a solution

I = u x 21/u
I/u = 1 x 21
21 = I/u

The problem is I'm completely drawing a blank. Any help would be appreciated.

Thanks,
Crazysah

2. Feb 15, 2012

### Crazysah

Anyone have any clue on this one?

3. Feb 15, 2012

### Fredrik

Staff Emeritus
a) What is her speed relative to the ground as she's going from A to B? Use this to calculate the time from A to B. Then do the same for the trip from B to A.

b) She will have to "aim" the plane a little to the right (south) of her target (B) in order to end up flying along a straight line from A to B. Use the Pythagorean theorem to find her speed relative to the ground as she flies towards B along that line.

That's all I have time for right now. Going to bed.

By the way, I don't know what you're doing here. What's I? Where did you get the number 21? Also (21u)/u=21, so your first equality says I=21, while the second and third say that I=21u.