Special Relativity. How to use the Lorentz Transformation?

[AlonsoMcLaren]

γ

Homework Statement

Stan is at rest on the Earth while Mary is moving away from the Earth at a constant speed
of 0.600c. Stan and Mary start their timers when Mary passes Stan (in other words, t = t' = x = x' = 0 at that instant).

(a) When Mary has traveled a distance of 0.900 *10⁸m according to Stan, what is the time according to Stan?

(b) At the instant Stan reads the time calculated in part (a), what does Mary’s timer read?

Homework Equations

Lorentz Transformation

The Attempt at a Solution

(a) is simple. I got it correctly. t=x/V=0.5s

I got (b) wrong. I plugged in the Lorentz Transformation:

x=0
γ=1.25
V=0.600c
t=0.5s

t' =γ (t-Vx/c2) = 0.625 s.

But the answer is 0.4s, which claims that x=0.900 *10⁸m, not 0.

However, at the instant Stan reads the time 0.5s from his clock, he and his clock are sitting on the earth, not 0.900 *10⁸m away from earth. So I do not think that x=0.

 

[Doc Al]

However, at the instant Stan reads the time 0.5s from his clock, he and his clock are sitting on the earth, not 0.900 *10⁸m away from earth. So I do not think that x=0.

The question should be interpreted as "At the instant Stan reads the time calculated in part (a), what does Mary’s timer read according to Stan?"

No, x ≠ 0. According to Stan, where is Mary at the moment in question?