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Problem 85 Hard Difficulty

An observer standing by the railroad tracks sees two bolts of lightning strike the ends of a 500 -m-long train simultaneously at the instant the middle of the train passes him at $50 \mathrm{m} / \mathrm{s}$. Use the Lorentz transformation to find the time between the lightning strikes as measured by a passenger seated in the middle of the train.

Answer

$-2.78 \times 10^{-13} \mathrm{s}$

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Video Transcript

Well, this is the equation for the Lorentz transformation. So in the question was saying that the Observer from the river tracks these two balls of lightning strike any and all train simultaneously. That means the time between the lighting strikes measured by the Observer for the railroad tracks should be zero. So I have a new question here. So eventually it was not a regimen here. T prime, you see, was next. We asked for IOC square. Next on here indicates that the times routes of and when the tea from here is the time between the lightning strikes measured by the passengers on the train. And we know the velocity is given as a 15 meter per second. And we know the aspirin, which is ah, Lanta training is a 500 meter. And when the sea is the speed of light which is equal to three times 10 are a meter per second. So now I can plug him back to the question to return being the prime, which is equal to negative, um, fee. I wish his 15 year per second and more about the X Prize, which is off 100 meter over a C. square, which is three times. Turn to a power eight meter per second to about two. And it will give us hey time between the lighting strikes that was measured by the observer from the train. You. So you go to negative 2.78 times 10 to the power off. Nick. 13 seconds. Remember? I said let us not here indicates that it's relative. So there, for the next time here doesn't mean about it was negative because we know that tightens the scale quantity. So what? We only care about its value. So the times always positive. Okay, so therefore, or have the time here should be go to the mat into of the team prime, which is equal to two points of a times 10 to the power off 9 13 seconds. And this is the answer for this question.

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