Two events occur in an inertial system K as follows. Event1: x 1 = a , t 1 =2 a

Question

Two events occur in an inertial system K as follows.

Event1: x1 = a, t1 =2a/c, y1 =0, z1 = 0
Event 2: x2 = 2.2a, t2 = 1.9a/c, y2 =0, z2 = 0

What is the velocity of the frame K' in which theseevents appear to occur at the same time? Express the velocityvector using thevariables a and c and theunit vectors, i, j, and k; for example, 2*i + 2*j is a vectorwhich bisectsthe x and y axes.
Have no idea as to how to solveit.
Any help isappreciated.
Have no idea as to how to solveit.
Any help isappreciated.

Explanation / Answer

this problem can be simplified by assuming the velocity u of K' isin the x- direction. then lorentz transformation from K to K' gives t ' = (t- ux/c^2) t' = (t- ux/c^2) if the events are simulatneous in K', 0 = t' = (t- ux/c^2) t= ux/c^2 u = t c^2/x = (a/c)(1.9-2)c^2/1.2a = -c/12 so K' moves parallel to the negative x direction with speed c/12.in vector notation, velocity = -(c/12) i

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