please answer fully Event A happens at the spacetime coordinates (1 lightsecond

Question

please answer fully

Event A happens at the spacetime coordinates (1 lightsecond (Is) is the distance light moves in 1 second) 1 lightsecond (is) is the /'A, x> V 3.70 s, 7.30 Is, 0.30 Is, 6.40 Is in the frame S, and event B happens at the spacetime coordinates, (t'B, -(1s, 27.0 I, 0.30 Is, -'B)=(-1.5 ls) X,B, y,B, s, 27.0 ls, 0.30 ls, 6.40 in another frame S' which is moving along the +x-axis at a speed u 0.610c relative to the frame S. Calculate the time interval between events A and B in frame S, and in frame S Number BA Number t'-t O In frame S, event A happens first then B, while in frame S'it is the opposite. O . O In frame S, event B happens first then A, while in frame S' it is the opposite. O In both frames S and S', event A happens first then B. In both frames S and S, event B happens first then A

Explanation / Answer

Given that

tA = 3.70 s

t'B = -1.5 s

u = 0.610c

gamma = 1 / [ 1 - (u/c)2 ]1/2 = 1 / [ 1 - (0.610c/c)2 ]1/2 = 1.262

Then tB = gamma * tA

   = 1.262 * 3.70 s

   = 4.67 s

Therefore tB - tA = 4.67 - 3.70 = 0.97 s

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Now calculate the tA' = gamma * tB'

   = 1.262 * -1.5

   = - 1.893 s

Therefore tB' - tA' = -1.5 - (-1.893) = 0.393 s

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In both frames S and S', event B happens first then A.

  

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