Can Frame S' Make Two Events Simultaneous?

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SUMMARY

The discussion centers on determining the velocity of frame S' where two events occur simultaneously, given their coordinates in frame S. The events are defined as Event 1 at (L, L/c) and Event 2 at (2L, L/2c). To find the velocity v of frame S', the equation t' = γ(t - vx/c²) is utilized, where γ is the Lorentz factor. By equating the time equations for both events, the velocity v can be solved, leading to a definitive solution for the time t' in frame S'.

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da_warped_1
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hi, wondering if anyone could give me a little help with this question

The space and time coordinates of two events are measured in frame S to be:

Event 1: x1 = L, t1 = L/c

Event 2: x2 = 2L, t2 = L/2c

(a) find the velocity of a frame S' in which both events occur at the same time?

(b) What is the time t' that both events occur in S'?

thanks
 
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Write t_1'=gamma(t_1-vx_1/c^2), and equate that to the same equation for
t_2'. Then, solve for v.
 

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