Relativity and Lorentz Transformations

  • #1

Homework Statement


Spaceship A of length 30m travels at 0.6c past spaceship B. Clocks in frame S' of spaceship A and S of spaceship B are synchronised within their respective frames of reference and are set to zero, so that t' = t = 0 at the instant the front of spaceship A passes the rear of spaceship B located at x' = x = 0. At this time a light flashes at the front of spaceship A.

a. When the light flash reaches the rear of spaceship A, what is the reading of a clock there?
b. What is the reading on the clock on spaceship B when according to an observer on B, the flash reaches the rear of A?

Homework Equations


Lorentz transformation formulas

The Attempt at a Solution


a. From spaceship A's POV, it is stationary. It measures proper length. Thus time t1' = 30m / speed of light. Is this correct?

b. Using Lorentz transformation of time,
t = γ(t' + ux'/c2)

x1' = -30, u = 0.6c and t1' from answer in a, I got t1 = 5.0*10-8 s. Does this work?

Thanks!
 

Answers and Replies

  • #2
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Homework Statement


Spaceship A of length 30m travels at 0.6c past spaceship B. Clocks in frame S' of spaceship A and S of spaceship B are synchronised within their respective frames of reference and are set to zero, so that t' = t = 0 at the instant the front of spaceship A passes the rear of spaceship B located at x' = x = 0. At this time a light flashes at the front of spaceship A.

a. When the light flash reaches the rear of spaceship A, what is the reading of a clock there?
b. What is the reading on the clock on spaceship B when according to an observer on B, the flash reaches the rear of A?

Homework Equations


Lorentz transformation formulas

The Attempt at a Solution


a. From spaceship A's POV, it is stationary. It measures proper length. Thus time t1' = 30m / speed of light. Is this correct?

b. Using Lorentz transformation of time,
t = γ(t' + ux'/c2)

x1' = -30, u = 0.6c and t1' from answer in a, I got t1 = 5.0*10-8 s. Does this work?

Thanks!
Yes.
 
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