Relativity and Lorentz Transformations

[little neutrino]

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!

 

[Chestermiller]

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.