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Misplaced Homework Thread -- Moved from the Technical Forums

**Summary::**Special relativity and Lorentz Transformations - I got this problem from a first-semester course at university. I have been struggling for a few days and decided to get some help.

A rocket sets out from x = x' = 0 at t = t' = 0 and moves with speed u in the negative x'-direction, as measured in S'.

After 1 year has elapsed in S', the rocket turns around.

According to observers in S, the rocket turns around at x = −1/5 light-year and it returns to the origin in S' at x = 4 light-years.

i) Calculate v/c.

ii) Calculate u/c.

iii) At what time in S does the rocket return to the origin in S'?