Quiz1_solution

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online