Two spaceships approach an observer from an equal distance and from an opposite direction with an equal speed in the observer's intertial reference frame O.(adsbygoogle = window.adsbygoogle || []).push({});

The speed of a spaceship in the intertial reference frame of the other spaceship S is 0.8c , what is the speed of one of the spaceships in O?

I proceeded as follows:

Let 2l' be the distance between the two spaceships in S.

In S the two spaceships will collide after a time t' = 2.5l'/c

Let F be the squareroot of 1 - v²/c² with v the sought speed

In O the two spaceships will collide when vt = l or vFt' = l'/F (O has to correct for what he perceives as the time dilations and space contractions of the measurements made in S)

Substituting we get the equation x(1-x²)=0.4 with x = v/c, if you solve the equation you conclude that this line of reasoning was wrong (but when we replace 0.4 by 0.375 we do get the right solution, which is 0.5c).

What happened?

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# Special relativity puzzle

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