Observer S reports that an event occurred on the x axis of his reference frame a

Question

Observer S reports that an event occurred on the x axis of his reference frame at x = 3.85 times 10^8 m at time t = 1.50 s. Observer S' and her frame are moving in the positive direction of the x axis at a speed of 0.400c. Further, x = x' = 0 at t = t' = 0. (a) What is the spatial coordinate of the event according to S'? 223673337.5 m (b) What is the temporal coordinate of the event according to S' 1.077 s If S' were, instead, moving in the negative direction of the x axis, find the following. (c) the spatial coordinate of the event according to S' 385089110.9 m (d) the temporal coordinate of the event according to S' 1.501 s

Explanation / Answer

observer S reports that an event occured on the x axis of his reference frame at x = 3.85*10^8

S' = Velocity of S * t - S

S' = (0.4* 3*10^8 * 1.5 + 3.85 *10^8)

S' = 5.65 *10^8 m

gamma factor = 1/sqrt(1-v^2/c^2)

gamma = 1/sqrt(1-0.4^2)

gamma = 1.091

S' = S*gamma

S' = 5.65 *10^8 *1.091

S' = 616415000 m

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part B: t' = t + (vx/c^2)

t' = 1.5 - (0.4*3.85 *10^8/(3*10^8)

t' = 1.5 + 0.513333

t' = 2.01333

Time t' = t*gamma

t' = 2.0133* 1.091

t' = 2.196 s

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