You say that distances are measured in light seconds but don't give any units for the speeds. Are we to assume they are measured in "light seconds per second"? Assuming that:
As seen from the earth, the two ships are closing with a net speed of 1.4 ls/s. They will cover the distance between them, 1 ls, in tc= 1/1.4 seconds. In that time, ship A will have moved a distance .8/1.4= 4/7 ls so xc= 4/7 ls.
As seen from A, ship B is closing on it at (.6c+ .8c){1+ (.6)(.8)/c^2}= 1.4c/1.48= 7/74 (of course, c is 1 ls per second). Also, as seen from A, the initial distance beween A and B is sqrt(- (.8c)^2/c^2)= sqrt(.36)= .6= 3/5 ls so they will pass, according to A, in (tc)'= (3/5)/(7/74)= 224/35 seconds. In that time, A will have moved .8(224/35)= 896/175 and (xc)' = 896/175 ls.
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Last edited by HallsofIvy; Mar 27th 2011 at 08:57 AM.
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