Quiz1_solution

Quiz1_solution - time T 1 = Τ + τ = (1+-29 29 = 1-/ But...

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1. (a) Using formula for relativistic addition of velocities, we have (measuring velocities to the right as positive) Velocity of spaceship B relative to A = - 0.5 c - (0.5 c ) 1- (- 0.5 c )(0.5 c ) / c 2 = - c/(1+1/4) = -4/5 c (moving to left) (b) Let proper length of spaceship B in its own rest frame be L B Then L B as seen by spaceship A = ( 1 - ω 2 / χ 2 29 Λ =30 m Where v is relative velocity of A and B = 4/5 c from part (a) So L B = 30/ 1 - 2 / 2 m = 30 / 1 - (4 / 529 2 m = 30 / (3/5) m=50 m (c) L A as seen by spaceship B = ( 1 - 2 / 2 29 A = (3/5) L A = 60m 2. By Professor’s clock, time quiz started is t = 0 If he sends signal at time T on his clock, spaceship is already at a distance vT from him. If it takes a further time t 0 on Professor’s clock for signal to reach spaceship, then ct 0 = ωΤ + ωτ 0 or t 0 = - Then , according to Professor’s clock, signal reaches spaceship at
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Unformatted text preview: time T 1 = Τ + τ = (1+-29 29 = 1-/ But the Professor knows that their clock has slowed down, so he calculates that it arrives at their time T , where T = 1-ω 2 / χ 2 Τ 1 = 1-2 / 2 1-/ = 1+ / 1-/ so T = 1-/ 1+ / Alternatively, one could view this as a relativistic (receding) Doppler shift problem: Suppose Professor emits signal periodically with time T His frequency would be f = 1/T If spaceship receives signal with period T (their time), frequency received by spaceship would be ′ f = 1 T = f 1-v / c 1+ v / c = 1 T 1-v / c 1+ v / c so T = T 1-v / c 1+ v / c...
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This note was uploaded on 12/07/2009 for the course PHYS phys 2d taught by Professor Hirsch during the Spring '08 term at UCSD.

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Quiz1_solution - time T 1 = Τ + τ = (1+-29 29 = 1-/ But...

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