Problem

(a) How long does it take the astronaut in Exampl…

04:58

Problem 15 Medium Difficulty

(a) How long would the muon in Example 28.1 have lived as observed on the Earth if its velocity was 0.0500$c$ (b) How far would it have traveled as observed on the Earth? (c) What distance is this in the muon's frame?

Answer

(a) $\Delta t=1.76 \mu \mathrm{s}$
(b) $L_{0}=264 \mathrm{m}$
(c) $L=229 \mathrm{m}$

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Physics 103

College Physics for AP® Courses

Chapter 28

Special Relativity

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Video Transcript

but an example 28.1 if the relative velocity of the Milan is 0.500 times the speed of light. So if we equals 0.500 times the speed of light, the life measured in the Beyonce ah frame of reference the proper time identity, not it is equal to 1.52 microseconds and 1.52 microseconds is 1.52 Motive Life. I tend to the parlor minus six seconds. The life of me on is measured by an art bond observer. Delta T is equal Do 4.87 microseconds Andi, since microbes tend to the bar minus six. There for Delta T equals 4.87 multiplied by 10 to the power minus six seconds on speed of flight C E called tree, find 00 multiplied by 10 to the power eat meter for a second. Well, ah, relight. A mystic factor is given by one divided by square root off one minus. We divided by sea whole square and this is the latest ick factor, and a greeting for time dilation is Delta T is equal to Delta t not divided by squared rode off one minus. We screamed, divided by C square and therefore identity is equal to relax, Ristic factor times don't pity not. And delta t noughties, though, uh, appropriate time. Well, uh, no. Let's find out the value of comma. Well, gamma is equal to, um one divided by square Root off, uh, one minus one minus, uh, 0.500 times the speed of light. Divided by sea, whole square. And therefore, government is equal to one divided by square boot off one minus. C square gets canceled with C square, and we're left with 0.5 00 hold scare. And finally, the have logistic factor. Is it cool too? 1111.155 And now, Dr T. Uh is equal to one 0.155 multiplied adult city not in delta T noticed 1.5 to multiply by 10 to the power minus six seconds. And therefore, don t t is a cool too, uh, 1.76 multiplier attend to devour minus six seconds seconds since 10 to the bar minus six is micro do before we have 1.76 micro seconds. Uh, no. Let's sold part B. Well, uh, we know it, and Mark equals we multiply by delta t on dhe. Therefore, a lot is equal to well, we is 0.500 Multiply by three, multiply by 10 to the power eight meters per second, multiplied by delta T and L titties 1.76 multiplied by 10 to the power minus six seconds. And therefore and Marty cools 264 maters. So a large equals 264 meters on DDE RC. Well, uh, embark. See, uh let's see who's got no eyes equal to 1.155 And we know that political to launch divided by gamma and now lick next leg in the values on is equal to and Lakis to 64 meters divided by gamma is 1.155 and therefore Alex equal to 229 meters

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