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An event occurs at x =60m, t =810-8 sec in a frame S (with y =0, z = 0). The frame S has a velocity of 3c/5 in the x direction with respect to frame...

An event occurs at x′ =60m, t′ =8×10-8 sec in a frame S′ (with y′ =0, z′ = 0). The frame
S′ has a velocity of 3c/5 in the x direction with respect to frame S. The origins of S and S′
coincide at t = 0, t′ = 0. What are the spacetime coordinates of the event in S?
The space and time coordinates of two events measured in the frame S are as follows:
Event 1: x1 =x0, t1 =x0/c, y1 =0, z1 =0
Event2: x2 =2x0, t2=x0/2c, y2 =0, z2 =0
(a) There exists a frame in which these events occur at the same time. Find the velocity of
this frame with respect to S.
(b) What is the value of t at which both events occur in the new frame?

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