Help with relativity and time dilation

AI Thread Summary
The discussion revolves around a physics problem involving time dilation and relativity, specifically regarding two firecrackers detonating at different times and locations as observed from two different frames of reference. The first observer sees the firecrackers detonate 4 seconds apart, while the second observer, moving relative to the first, perceives them detonating at locations separated by 3 light-seconds. The key challenge is to determine the time interval between the detonations as observed by the second observer and to calculate the relative speed of this observer. Participants emphasize the need to apply Lorentz transformations to relate the measurements of time and distance in different frames. Understanding these transformations is crucial for solving the problem accurately.
jaterp
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This problem i got for school has been driving me crazy >.<

"As seen by one observer, two firecrackers are set off at the same place but separated by 4 seconds in time. As observerd by a second observer, moving with respect to the first, the two firecrackers detonate at places separated by 3 light-seconds in space. As observed by this second observer, how much time is there between the two detonations?
How fast is this second observer moving with respect to the first?"

So basically for the second observer, he sees the detonation happen at different places coz he's moving right ? but where am i suppose to go from there ? I solved for v with time dilation thinking that second observer sees the time as 3 seconds but when i re-read the question i realized i totally misunderstood it and that it was distance between the detonation. Any sort of help will be really appreciated ^^
 
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Start by writing the Lorentz transformations that relate distance and time measurements made in different frames.
 
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