Solving the Rocket Ship Problem

[strangequark]

Homework Statement

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...

Homework Equations

Length contraction, and the lorentz transforms.

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?

 

[learningphysics]

EDIT: Yes, you're right.

 

[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...

 

[learningphysics]

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...

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

 

[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!