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Check yourself Answers

1B and C because there is no acceleration.

29 m s−1 due south.

3No, we have to subtract the time it took light to get to the observer.

4If A and B are separated by a distance Δx, the time it would take the photon to get to B would be Δ x c. The spacetime interval is then c 2(Δ t)2−(Δ x)2=c 2(Δ x)2 c 2−(Δ x)2=0.

5 aYes

bYes

cNo

6The spacetime diagram in Figure 6.47 shows that the left tree was hit first. Photon lines from the strikes arrive at the rocket at the same time.

7In frame S the light will reach the spacecraft in a time t given by 0.6c t + c t = 4 ⇒ c t = 2.5 ly when the spacecraft is at x=0.6 c×2.5 c=1.5 ly. The gamma factor is 1.25 and so c t′=1.25×(2.5−0.6 c c×1.5)=2.0 ly.

Figure 6.47: For check yourself question 6.