Special Relativity

1. Sep 8, 2007

strangequark

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

Two rocket ships, each with a rest length of 100 meters. Rocket 1 is at rest in frame S and has nose at x=0, tail at x = +100 meters. Rocket 2 is at rest in frame S' and has nose at x' = 0 and tail at x'=-100 meters. Suppose S' moves with speed V in the positive x direction realtive to S. Event A synchronizes the two frames (x=x'=t=t'=0), and event B is when the tail o rocket 2 passes the nose of rocket 1 at time t=2.5 microseconds in frame S. Find the speed V...

2. Relevant equations

Length contraction, and the lorentz transforms.

3. The attempt at a solution

What I did was say that the distance rocket 2 moved as observed from the S frame was:

$$x_{b}=\frac{L_{0}}{\gamma}$$

Then the velocity would be distance over time, or:

$$v=\frac{\frac{L_{0}}{\gamma}}{t_{B}}$$

Then I solve for v and get something like .133c for my relative velocity...
Am I on the right track here?

2. Sep 8, 2007

learningphysics

EDIT: Yes, you're right.

Last edited: Sep 8, 2007
3. Sep 8, 2007

strangequark

Awesome, thanks!... while you're here, the second part of the problem states that event C is the event that the nose of rocket 2 passes the tail of rocket 1 and asks for the time coordinate with respect to the S frame...

I'm thinking that I can just take the length of the ship (100 m) and divide by the relative velocity... but it seems too simple...

4. Sep 8, 2007

learningphysics

Yes, that will give you the answer. BTW I get 0.132c for part 1.

Last edited: Sep 8, 2007
5. Sep 8, 2007

strangequark

Sorry, yeah, I end up with .132254c also.

Great... maybe I'm not as confused about this as I feel sometimes. I tend to think myself into circles with relativity...

I really appreciate you taking the time to look at this with me... Thanks!