Usual situation in which a primed reference frame passes an un-primed referance

Question

Usual situation in which a primed reference frame passes an un-primed referance frame, in the common poistive direction of the x and x' axes, at a constant relative velocity of magnitude v. We are at rest in the unprimed frame, the observer is also at rest in the primed frame. The figures indicate that the events A and B occur at the following spacetime coordinates as measured in our unprimed frame and in the observers primed frame.

Event Un-primed Primed
A (xA, tA) (x'a, t'A)
B (xB, tB) (x'B, t'B)

In our frame event A occurs before event B, with temporal separation delta t= tB-tA = 1.0 us and spatial seperation delta x = xB-xA = 400m. Let t' be the teemporal sepration of the events according to the observer.

a) Find an expression for delta t' in terms of the speed paramter B(=v/c) and the given data.

Explanation / Answer

given that t =  tB-tA = 1.0 s x = xB-xA = 400m
the lorentz tranformation equations for pair events
t1 = (t -vx/c2) where = v/c t1 = (t -x/c)      = ( 1x 10-6s - ( 400 m)/ 2 .998 x 108 m/s) the lorentz tranformation equations for pair events
t1 = (t -vx/c2) where = v/c t1 = (t -x/c)      = ( 1x 10-6s - ( 400 m)/ 2 .998 x 108 m/s)

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