When and Where Will Spaceships #1 and #2 Meet in Special Relativity?

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Spaceship #1 travels at 0.2c, while Spaceship #2 moves at 0.6c, starting 3 x 10^9 m behind. The relative velocity of Spaceship #2 in the inertial reference frame of Spaceship #1 is calculated to be approximately 0.7143c, though this value exceeds the speed limit set by special relativity. The recommended approach is to first determine when and where the spaceships will meet in reference frame S using classical mechanics, then apply the Lorentz transformation to find the corresponding time in the frame of Spaceship #1. This method ensures accurate calculations within the constraints of special relativity.
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Spaceships--special relativity

Homework Statement


Spaceship #1 moves with a velocity of .2c in the positive x direction of reference frame S. Spaceship #2, moving in the same direction with a speed of .6c is 3 x 10^9 m behind. At what times in reference frames S, and in the reference frame of ship #1, will 2 catch up with 1.


Homework Equations





The Attempt at a Solution


I solved for the relative velocity of ship 2 in the IRF of ship 1. I got .7143c. I'm not really sure where to proceed from here. Any ideas?
 
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The spaceships move in the same direction, so the relative velocity can't be larger than 0.6c. I don't think it's very useful to compute anyway.

Just compute when and where the spaceships catch up in frame S. This can be done in the classical way. Then use the lorentz transform to find the time in the frame of
ship #1
 

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