Suzanne observes 2 light pulses to be emitted from the same location, but separated in time by 3μs. Mark sees the emission of the same two pulses separated in time by by 9μs.
a) How fast is Mark moving relative to Suzanne?
b) According to Mark, what is the separation in space of the two pulses?
Time dilation, Lorentz transforms
The Attempt at a Solution
My first attempt had Mark as the 'primed' observer, since I am used to that frame moving, and they are asking about Mark's relative velocity to Suzanne, and I got an answer that didn't make any sense for v.
I realized that since Mark is observing a larger time interval than Suzy, she must be in the 'primed' frame for Δt = γΔt' to make any sense. So I did it that way, and found a v of .943c which I think is correct. (The answers to this question are not in the back of the book)
But as for the question 'How fast is Mark moving relative to Suzanne' I am not sure. Is the answer to this question -.943c, since Suzy's frame is moving away from Mark in the positive direction?
Suzy observes the pulses to be emitted from the same location, so Δx' = 0. Mark's observation however, Δx, is going to be non-zero, since the pulses are moving in his frame.
So in this case, would I just use (vt = d) .943c * 9μs ≈ 2.5km ? or is there something about the speed of light and the pulses moving away from him that would distort this answer? Or should I just assume he observes the pulses instantaneously? If the latter, then would 2.5km be the correct answer?
Thanks for the help in advance..