Homework Help -- Relative Velocity

[Jade45]

<Moderator note: moved from technical forums, so no template>

Problem: Two trains (A and B) are moving along parallel tracks at different speeds. A person sitting on train A looks out the window and sees two things happen: a firecracker explodes right outside his window, and, exactly 1.0 microseconds later, a woman standing by the tracks 600m ahead of him drops her umbrella. Now, the passenger on train B, moving at a different velocity from train A, observes these same two events and also concludes that they occurred 600m apart. Based on this information, you should be able to determine the relative velocity v between the two trains.

Attempt: I understand that this is from the reference point of the person on Train A so the Lorentz Expression would be:
Δx= XB - XA = 600m -0m
Δx'=ϑ(Δx -v*Δt)
ϑ=1/√(1-β^2)
I guess I take the Lorentz transformation equation and solve for v and then plug in the numbers.
Am I on the right track or completely wrong?

 

[Chestermiller]

<Moderator note: moved from technical forums, so no template>

Problem: Two trains (A and B) are moving along parallel tracks at different speeds. A person sitting on train A looks out the window and sees two things happen: a firecracker explodes right outside his window, and, exactly 1.0 microseconds later, a woman standing by the tracks 600m ahead of him drops her umbrella. Now, the passenger on train B, moving at a different velocity from train A, observes these same two events and also concludes that they occurred 600m apart. Based on this information, you should be able to determine the relative velocity v between the two trains.

Attempt: I understand that this is from the reference point of the person on Train A so the Lorentz Expression would be:
Δx= XB - XA = 600m -0m
Δx'=ϑ(Δx -v*Δt)
ϑ=1/√(1-β^2)
I guess I take the Lorentz transformation equation and solve for v and then plug in the numbers.
Am I on the right track or completely wrong?

Looks OK.

 

[PAllen]

The answer is kind of amusing ...