Problem

Unreasonable Results (a) Find the value of $\gam…

03:10

Problem 17 Medium Difficulty

(a) How fast would an athlete need to be running for a 100 -m race to look 100 yd long? (b) Is the answer consistent with the fact that relativistic effects are difficult to observe in ordinary circumstances? Explain.

Answer

(a) $v=1.22 \times 10^{8} \mathrm{ms}^{-1}$
(b) Yes.

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Physics 103

College Physics for AP® Courses

Chapter 28

Special Relativity

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Video Transcript

the proper distance and not is equal to 100 meters. A launch is equal to 100 meters on Dhe. The contract ID land panel is equal to 100 yards 100 yards on dhe. We know that one yard, uh, one yard is equal to 0.914 for, uh, meters. And therefore, um, we have, uh l equals 100 yard. Let's go. 100 yards and emitters. So 100 yards multiplied by zero point mind 144 due by the by one yard. And this is, uh, Peter, and therefore, contract ID land physical to 91 point four for meters. Uh, we know that l equals contacted. Length is equal to a smart divided by, ah, land mystic factor. We have not, um, a lot. And, uh, a lot is, huh? A lot of physical 200 meters. I'm great meters divided by relativistic character comma and solving for a relativistic factor. Goemon is equal to, um 100 meter divided by a 91.44 meters on 91 point for four meters on DDE. This gives us 1.9 for 1.94 So their linguistic factories equal to one point 094 Well, we know that on a latticed ick factor is equal to one divided by square root off one minus We divided by sea Hold square on solving for re relative velocity. We is equal to see times, huh? Square root off one minus one, divided by gamma whole square. And let's a substitute Relax, mystic factor. And on this tram is equal to see into square root off one minus one, divided by He had relied mystic factories 1.94 and we have square. And this gives us we Is he cool too? Zero point the 0.406 times the speed of light and the speed of light is huh? A three multiply attentively power eight Therefore being a still point for 06 multiplied by 3.0 multiplied by 10 to the power eat and therefore the lost Easy Cool too 1.22 Multiply by 10 to the power eat meter or second on Duh In part B Um yes, a person cannot run with this speed. Well, a person person cannot run with speed Cannot run with this speed with this speed doing. For uh, the answer is consistent with the fact that relativistic effects are difficult to observe in ordinary circumstances. So in ordinary circumstances, in ordinary circumstances in ordinary circumstances related a sticky facts, real activists kick related a stick effect are not obvious.

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