Frames S and S\' are moving relative to each other along the x and x\' axes. The

Question

Frames S and S' are moving relative to each other along the x and x' axes. They set their clocks to t = t' = 0 when their origins coincide. In frame S, event 1 occurs at x1 = 4 c · y and t1 = 1 y and event 2 occurs at x2 = 8.0 c · y and t2 = 0.5 y. These events occur simultaneously in frame S'.

(a) Find the magnitude and direction of the velocity of S' relative to S.

(b) At what time do both of these events occur as measured in S'?
y

(c) Compute the spacetime interval ?s between the events.
c · y

(d) Is the interval spacelike, timelike, or lightlike?

(e) What is the proper distance Lp between the events?
c · y

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Explanation / Answer

Vector sums:

let i = unit vector
let j = unit vector perpendicular to i

Velocity of A relative to C = Velocity of A Relative to B + Velocity of B relative to C

Vac = Vab + Vbc
a) Vac = 3i + 5j
Magnitude of Vac = |Vac| = sqrt(3^2 + 5^2) = sqrt(34)
Direction of Vac = atan(3/5) relative to the direction of water movement

b) Vac = 1i + 6j
|Vac| = sqrt(1 + 6^2) = sqrt(37)
Direction of Vac = atan(1/6) relative to the direction of water movement

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