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I am looking at a special relativity question but none of the choices make sense. If a clock is racing by you at the speed 45 of light speed and you determine that 30 minutes go by on the clock, how many minutes will have gone by on your own clock? The choices are as follows:

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My attempt: $$ \Large t' = \frac{t}{\sqrt{1-\frac{v^2}{c^2}} }$$Then plugging in$$ \frac{30}{\sqrt{1-\frac{(.45c)^2}{c^2}} }= 33.59 $$ Converting minutes to seconds doesn't change the answer.

The answer is supposed to be $50$ minutes.

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The typo is that the speed is 4/5 of light speed. This will get you answer D.

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Speaking in terms of physics, I believe your answer of 33.59 minutes is correct.

If you were forced to choose one of the provided answers, you should of course choose (d), however. You can eliminate (a) and (b) because you know their clock is dilated relative to yours. Similarly, you can eliminate (c) because at speed $0.45c$, some dilation will occur. So speaking strictly conceptually, choice (d) is the only possible answer (although it is far too high).

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  • $\begingroup$ Thank you for your response. Can you also look over my work on a similar problem. A clock moves past you at a speed of 0.9 How much time passes for you for each second that elapses on the moving clock? I got $ t= \frac{1}{ \sqrt{ 1 - \frac{(.90c)^2}{ c^2}}} (1) = 2.29~ {\rm sec}$ $\endgroup$ – john Dec 31 '17 at 21:47
  • $\begingroup$ I also get 2.29 seconds. $\endgroup$ – zhutchens1 Dec 31 '17 at 21:49
  • $\begingroup$ I also have an issue with this article here. It says that an observer on a moving rocket sees a clock on earth running fast. That's false. The rocketman should see an earth bound clock running slow, unless he could skip using a telescope and 'instantaneously' see the clock. There is supposed to be a symmetry here. They should both see each other's clocks running slow. Full article. $\endgroup$ – john Dec 31 '17 at 21:58
  • $\begingroup$ Yes you are right. Each observer should perceive their own clock to tick normally, and they should see each other's clocks as ticking too slowly. It has to be this way because there is no way to physically distinguish who is moving and who is at rest -- that's one of the postulates of SR. $\endgroup$ – zhutchens1 Dec 31 '17 at 22:01
  • $\begingroup$ @john That article has many problems. Most of them are a matter of poor, troubling phrasing, but there is, as you point out, at least one error. $\endgroup$ – garyp Dec 31 '17 at 23:42

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