γ1. The problem statement, all variables and given/known data
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 *10^{8}m 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?
2. Relevant equations
Lorentz Transformation
3. 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 (tVx/c2) = 0.625 s.
But the answer is 0.4s, which claims that x=0.900 *10^{8}m, 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 *10^{8}m away from earth. So I do not think that x=0.
