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HW 14 Problem 9

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Keilah, in reference frame S, measures two events to be simultaneous. Event A occurs at the point (31.0 m, 0, 0) at the instant 9:00:00 Universal time on January 15, 2010. Event B occurs at the point (120 m, 0, 0) at the same moment. Torrey, moving past with a velocity of 0.830ci hat bold, also observes the two events. In her reference frame S', which event occurred first?

event A

Or

event B  


What time interval elapsed between the events?

asked Nov 21, 2013 in Intro College Physics by anonymous

1 Answer

0 votes

We can use Lorentz transformation to solve this problem. Set up the original events in the x-t frame and find the new set of coordinate in x'-t' frame which is traveling at v in the positive x direction. You may set the time to be 0 for the events A and B to happen in the x-t frame. I would recommend to use a table to record all the known and unknown variables so we can see clearly what are needed. See a solution slides show below:

Events simultaneity lorentz transformation

 

We can also use space time diagram to find the order of events:

space time events order

On the space diagram, the lines parallel to x' are events happened at the same time in t'. From the intersections on ct' axis from the two x'-parallel lines going through A and B, we can see the line going through B intersect ct' at an earlier t' and therefore, in x'-t' frame, B happens first.  

answered Nov 23, 2013 by PhysicsDude (21,750 points)
Doubt regarding your diagram
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