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A question about relativity
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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 hes moving right ? but where am i suppose to go from there ? any help will be appreciated ^^ |
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Re: A question about relativity
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on 2005-12-18 07:00:29 |
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I can do the setup for you but the algebra got me stuck. First, define the reference frames. Let S be the reference frame of the first observer, and S` be the reference frame of the Important: the velocity of S` relative to S is unknown! second observer. Second, define the events. Let E0 be the light from the first firework being seen by the the observer in S. Let E1 be the light from the second firework being seen by the observer in S. Now, describe each event in terms of S and S`. E0: t=0s, x=0cs, t`=0s, x`=0cs E1: t=4s, x=0cs, t`=?s, x`=3cs We know the Lorentz Transformation for position: x`=(x-vt)/sqrt(1-(v/c)^2) Plug in what we know for E1 and I get 3cs=4v/sqrt(1-(v/c)^2) Solve for V and you can solve for time by using the Lorentz Transformation for time: t`=(t-vx/c^2)/sqrt(1-(v/c)^2) Im not too sure about how to do that bit of algebra, im sure you can figure it out with MathCad if you have that installed. 
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Re: A question about relativity
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on 2005-12-18 09:11:34 |
Ranger What about the doppler shift with the second observer in motion?  |
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Re: A question about relativity
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on 2005-12-18 11:32:33 |
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the question didnt ask about wavelength, but that would be another neat problem to do.
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Re: A question about relativity
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Have ya ever thought that if you think to much..................you'll explode.(please don't write some complicated algebra on how you can't explode by just thinking) I mean wow you must really retain a lot of information to give an answer to that. My own answer is: Man number one was trying to prove his theory. Man number two was jealous of his friend's theory and lied. |
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Re: A question about relativity
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on 2005-12-18 17:15:58 (edited 2005-12-26 06:18:22)
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I have to say Kotsuo your answer does show a different approach. Gendou, don't let Ranger get inolved. You'll wind up think you're in a classroom. Kotsuo, I liked your answer so I un-deleted it, I hope you don't mind. |
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Re: A question about relativity
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I'm not sure, but i'm pretty positive you can't solve that unless you have the velocity of the second observer. So I think you can't evaluate for the difference in perspective unless you are given the velocity, because I'm not sure how you would derive it.
"Death destroys a man, the idea of death saves him." E.M Forster
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