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Chapter 35: Problem 21
Find the speed of light in feet per nanosecond, to three significant figures.
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Two stationary space stations are separated by a distance of \(100 .\) light- years, as measured by someone on one of the space stations. A spaceship traveling at \(0.950 c\) relative to the space stations passes by one of the space stations heading directly toward the other one. How long will it take to reach the other space station, as measured by someone on the spaceship? How much time will have passed for a traveler on the spaceship as it travels from one space station to the other, as measured by someone on one of the space stations? Round the answers to the nearest year.
Which quantity is invariant-that is, has the same value-in all reference frames? a) time interval, \(\Delta t\) d) space-time interval, b) space interval, \(\Delta x\) \(c^{2}(\Delta t)^{2}-(\Delta x)^{2}\) c) velocity, \(v\)
The most important fact we learned about aether is that: a) It was experimentally proven not to exist. b) Its existence was proven experimentally. c) It transmits light in all directions equally. d) It transmits light faster in longitudinal direction. e) It transmits light slower in longitudinal direction.
If a muon is moving at \(90.0 \%\) of the speed of light, how does its measured lifetime compare to when it is in the rest frame of a laboratory, where its lifetime is \(2.2 \cdot 10^{-6}\) s?
Consider two clocks carried by observers in a reference frame moving at speed \(v\) in the positive \(x\) -direction relative to ours. Assume that the two reference frames have parallel axes, and that their origins coincide when clocks at that point in both frames read zero. Suppose the clocks are separated by distance \(l\) in the \(x^{\prime}-\) direction in their own reference frame; for instance, \(x^{\prime}=0\) for one clock and \(x^{\prime}=I\) for the other, with \(y^{\prime}=z^{\prime}=0\) for both. Determine the readings \(t^{\prime}\) on both clocks as functions of the time coordinate \(t\) in our reference frame.
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