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Can i use proper time in such example ?

IE: Imagine We have a rocket ''Ra'' moving with respect to earth at 0,8c and a ''Rb'' rocket moving with respect to earth at 0,98c. Rb is following Ra until they meet. The distance , reference from earth, between Ra and Rb is 10000 meters. numerical values just to show thw problem. 1. what is the time to the meet, reference to earth? 2. what is the time to the meet, reference to rockb Rb?

part 1.

$t = 1,85. 10^{-4}$

part 2( my problem to solve).

my idea 1: using velocity composition and length contraction: $time = 7,9. 10^{-6} s$

My second idea: using proper-time $T^2 = t^{2} - x^{2} = t´^{2} - x´^{2}$ with $x = 10000m$ and $t = 1,85. 10^{-4}$ (part 1) and $x´^2 = \frac{x^{2}}{gama^2}$

HENCE, $time = 1,82.10^{-4}$ s

Whats the problem with my ideas? =/ Thanks.

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Welcome to Physics.SE! I'm going to close this on the basis of our homework policy (i.e. it looks like an exercise right now). It may be possible for you to re-write this in a way which would make re-opening possible. If you are going to embark on that course you should probably also convert your math to use the MathJax rendering engine (i.e. write LaTeX). – dmckee♦ Apr 4 '12 at 23:15
How can I improve it to open? – AlexandreH Apr 5 '12 at 2:03
It might elucidate physical concepts better by replacing numerical values with unknown variables and more words. Also, show how you obtain the answer to part 1. – leongz Apr 5 '12 at 3:00
Your problem is that you are neglecting relativity of simultaneity. You need to draw the space-time diagram for the two rockets, and you'll see that the lowest leg of the triangle is only horizontal from the Earth frame. I don't think this is homework, by the way, because it is confusion relating to a homework problem, not the problem itself. – Ron Maimon Apr 5 '12 at 3:00
As I said,I answered part 1 just using $time = space/velocity$ bEcause to the earth, its trivial. Ron Mainon, I don´t succeed in the picture of space-time, i´ts complicated to me. sO, i don´t understand why the velocity composition get a good answer, i think, and doesnt the proper time. =/ – AlexandreH Apr 5 '12 at 3:09
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closed as too localized by dmckee♦ Apr 4 '12 at 23:17

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