Muon Decay at t=2.2x10^-6s in Frame s': Coordinates and Time

[s7b]

consider two frames s and s' where s' is moving with velocity vector (0.9c,0,0) with respect to s frame. At time t=t'=0 the origin of the two frames coincide. At time t=2.2x10^-6s a muon decays at coordinates (100,0.8,1.0) meters in the s frame.

a) At what time and coordinates does the muon decay in frame s''?


Attempt:

For this question I used the formula for time dilation to find the time the muon decays in the frame s''.

I used t=(gamma)(proper time) where the proper time is the 2.2x10^-6

How do I go about finding the new co-ordinates??

 

[granpa]

https://www.physicsforums.com/showthread.php?t=257689