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Moved from a technical forum, so homework template missing.

I'm doing some exercises about special relativity and one of them asks to find the speed in an arbitrary frame of reference (1) in such a way that it perceives two events at the same time that didn't happen simultaneously in other frame of reference(2).

Is it correct to state that if the distance between the two events in the frame (2) is ##ct_{2}##, and the first event happened when ##t_{2} = t_{1} = 0##, an observer in the frame of reference (1) could only perceive these two events as simultaneous if it were traveling at the speed of light?

What I tought was

##t' = \gamma (t - \frac{ux}{c^2})##

Since ##x = ct_{2}##

##t' = \gamma (\frac{x}{c} - \frac {ux}{c^2})##

For this to be ##0##: ##\frac{x}{c} = \frac{ux}{c^2} \therefore u = c##

Is there anything incorrect here?

Is it correct to state that if the distance between the two events in the frame (2) is ##ct_{2}##, and the first event happened when ##t_{2} = t_{1} = 0##, an observer in the frame of reference (1) could only perceive these two events as simultaneous if it were traveling at the speed of light?

What I tought was

##t' = \gamma (t - \frac{ux}{c^2})##

Since ##x = ct_{2}##

##t' = \gamma (\frac{x}{c} - \frac {ux}{c^2})##

For this to be ##0##: ##\frac{x}{c} = \frac{ux}{c^2} \therefore u = c##

Is there anything incorrect here?

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