An event occurs at x = 100m, and lasted for t = 5.0 mu s in one frame of referen

Question

An event occurs at x = 100m, and lasted for t = 5.0 mu s in one frame of reference. Another frame is moving at 0.995c in the negative x direction. The origins coincide at t = 0 and clocks in the second frame are zeroed when the origins coincide. What is the coordinate and duration of the event in the second frame are? Star A is moving away from us (along the x-axis) at a speed of 0.8 c. Star B is moving away from us in the opposite direction (also along x-axis) at a speed of 0.4c. The speed star A as measured by an observer on star B is:

Explanation / Answer

Q3.

x coordinate of the even in second frame=-100*sqrt(1-(v/c)^2)

=-100*sqrt(1-0.995^2)=-9.9875 m

time duration=5 us/sqrt(1-0.995^2)=50.063 us

Q4.

velocity of A w.r.t. stationary observer

=Vao=0.8c

velocity of B w.r.t. stationary observer=Vbo=-0.4*c

then using relative velocity in relativity concept:
velocity of A w.r.t B

=(Vao+Vbo)/(1+(Vao*Vbo/c^2))

=(0.8*c-0.4*c)/(1-0.8*0.4)

=0.58824*c

hence for an onserver at B, A will appear to move at 0.58824*c speed.

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