On average, how far away are galaxies that are moving away from us at 2.0% of the speed of light?
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Final Answer

0.30 Gly0.30 \textrm{ Gly}

Solution video

OpenStax College Physics for AP® Courses, Chapter 34, Problem 5 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. Based on our measurement of the speed at which our galaxy is receding from us, which we are told is two percent the speed of light or in other words, 0.020 times c let's figure out what the distance to the galaxy must be given that we know Hubble's constant. So equation number 1 from chapter 34 is that the recessional velocity of the galaxy is Hubble's constant times its speed away from us and so we can solve for d by dividing both sides by H naught. And so we have a speed of 0.020 times the speed of light converted into kilometers per second and we need to do that because the Hubble's constant has strange units including kilometers per second and when we do this calculation, our final units will be megalight-years. So we have 3 times 10 to the 2 megalight-years or 0.30 gigalight-years is the distance to the galaxy.