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Problem 9 Medium Difficulty

A spaceship travels at constant velocity from Earth to a point 710 ly away as measured in Earth's rest frame. The ship's speed relative to Earth is $0.9999 c .$ A passenger is 20 yr old when departing from Earth. (a) How old is the passenger when the ship reaches its destination, as measured by the ship's clock? (b) If the spaceship sends a radio signal back to Earth as soon as it reaches its destination, in what year, by Earth's calendar, does the signal reach Earth? The spaceship left Earth in the year 2000.

Answer

(a) $A g e=30 \mathrm{yr}$
(b) Not yet, will arrive on 3420

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Video Transcript

the question. I was asking us how old the passengers be as it was measured by the ship's clock. Well, we know this kind of question is dealing with the time dilation musicality because who, grandma times Delta teaser. Okay, come on. The Lawrence factor, which is he was won over square one, minus the square overseas. Where? Okay. And since the question was asking us the time measured by the A spaceship clock, which means just asking dalati zero and gelati year means the time on earth. Okay, so we have done that. He zero is equal to, uh she goes down. That's he over gun. Okay, which is equal to square root one minus the square was C square times duality. Okay, but we know that me the speed of a spaceship he's given as zero point ni my ni. I see. Okay. And Donald t, this game has ah, memory. The distance on a spaceship to a point is, uh, 710 light years. So light years is the distant that light travel warriors. So she's a 710 Linus. Name is the time. Takes a light to travel. There is 710 years. Okay. And therefore we re plugging. The values will have. Don t zero is equal to square one minus Joe boy. 99 My night C square over C square. Okay. And times the time from a measure from Earth, which is 700 attain years. Okay. And you should give us Donna T zero is about 10 years. And remember, the passenger was 20 years old. So that means during his trip during his trip, eventually, he would become 30 years old on a spaceship. So it's 20 years plus 10 years, which is 30 years. Yeah, so? So he'll be 30 years old. Simple question. Be I was asking us will be the year on earth calendar when a signal was, uh, send back was sending back to Earth. Well, we know he takes 710 years. Well, I to travel at a points. So in order to travel back, it took another seven, 110 years. Okay, so the total denial, because his 710 years times two okay, which is 14 20 years. Oh, yeah. This is a 1420 years and sees the Earth with at 2000. You're the year 2000 Amy's way when the signal rich fact to the earth will be 2000 years less 14 20 years, which is equal to 34 20 years. Okay, so we way rich back the years on counter will be 34 20. Okay? The reason why he took 7 10 years to a trial back and forces because the signal is traveling a speed of lights, OK, and these are my answers for these questions. Thank you.

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