hw09_sol - 27. (a) One thing Einsteins relativity has in...

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27. (a) One thing Einstein’s relativity has in common with the more familiar (Galilean) relativity is the reciprocity of relative velocity. If Joe sees Fred moving at 20 m/s eastward away from him (Joe), then Fred should see Joe moving at 20 m/s westward away from him (Fred). Similarly, if we see Galaxy A moving away from us at 0.35 c then an observer in Galaxy A should see our galaxy move away from him at 0.35 c , or 0.35 in multiple of c . (b) We take the positive axis to be in the direction of motion of Galaxy A, as seen by us. Using the notation of Eq. 37-29, the problem indicates v = +0.35 c (velocity of Galaxy A relative to Earth) and u = –0.35 c (velocity of Galaxy B relative to Earth). We solve for the velocity of B relative to A: 2 ' / / ( 0.35) 0.35 0.62 1 / 1 ( 0.35)(0.35) uu c v c cu v c −− == = , or | '/ | 0.62. uc =
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(b) In the armada’s rest frame (called S a ), the velocity of the messenger is v vv vv c cc c c a a ' / .. (. ) (. )/ = = = 1 095 080 10 9 50 8 0 0 625 22 Now, the length of the trip is 0 1.0ly '1 . 6 0 y . ' 0.625 L t vc == = (c) Measured in system S , the length of the armada is L L = 0 2 1 060 γ .( . ) . , ly ly so the length of the trip is 0.60ly 4.00 y . 0.95 0.80 ma L t c c = −− 31. (a) In the messenger’s rest system (called S m ), the velocity of the armada is v vv c c c m m ' / / = = =− 1 8 00 9 5 0 625
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hw09_sol - 27. (a) One thing Einsteins relativity has in...

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