Andrew is at rest in frame S and observes Bob moving to the right (frame S0 is
bobs rest frame) with speed v. On the ground, a distance L to the right of Andrew, is a lamp.
At the instant that bob passes Andrew (as observed in frame S), the lamp emits a flash of light
At what time (in frame S0) does the light reach bob?
The Attempt at a Solution
Ive tried this problem using two methods, though I am not sure which one is correct, if any.
let the instant that bob passes Andrew occur at t=0 and x=0
in frame S, bob recieves the light at t = L/(v + c), but bobs clock runs slower by a factor of gamma
so in S0, bob recieves the light at t'=γ*L/(v + c).
But wouldnt this imply that in bobs frame, the flash moves at velocity v+c? which violates the postulate that the speed of light is the same in any frame.
in bobs frame, the lamp is moving towards him at speed v, so the distance to the lamp in frame S0 is contracted to L'=(1/γ)*L.
and in S0 the flash travels at speed c, so in S0, the flash reaches bob at time t'= L/(c*γ)
i am leaning towards attempt 2, however in bobs frame, would the flash of light occur before bob passes andrew?