Help with relativity and time dilation

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SUMMARY

The discussion centers on a physics problem involving relativity and time dilation, specifically analyzing the observations of two observers regarding the detonation of firecrackers. The first observer notes the detonations occurring 4 seconds apart, while the second observer, moving relative to the first, perceives the detonations occurring at different spatial locations, separated by 3 light-seconds. To solve this problem, participants emphasize the importance of applying Lorentz transformations to relate time and distance measurements across different inertial frames, ultimately leading to the calculation of the time interval between detonations as perceived by the second observer.

PREREQUISITES
  • Understanding of Lorentz transformations in special relativity
  • Familiarity with the concepts of time dilation and length contraction
  • Basic knowledge of inertial reference frames
  • Ability to perform calculations involving the speed of light
NEXT STEPS
  • Study the derivation and application of Lorentz transformations
  • Learn about time dilation effects in special relativity
  • Explore examples of length contraction in moving reference frames
  • Practice solving problems involving relative motion and simultaneity
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Students of physics, educators teaching relativity concepts, and anyone interested in understanding the implications of time dilation and spatial separation in different inertial frames.

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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