This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Physics 105 Problem Set 12 Solutions Each problem is worth 3 points Problem 9.1 An observer sees two spaceships flying apart, each with speed . 99 c relative to the observer. What is the speed of one spaceship as viewed by the other? In order to solve the problem one needs to go to the reference frame related to one of the spaceships and find the velocity of the second one. This is done by the relativistic law of velocity addition v = v 1 + v 2 1 + v 1 v 2 /c 2 ; where v 1 = 0 . 99 c = v 2 . Performing the substitution we get v ' . 99995 c. Problem 9.2 A laser beam is aimed at angle above the horizontal axis (the xaxis) as measured in the rest frame of the laser. An observer in a different reference frame sees the laser moving at very high velocity, v , along the xaxis in the observers frame. What is the laser beams angle above the horizontal in this observers frame? (You may leave your answer in terms of = v/c and the Lorentz factor, , as well as v and .) Hint: this problem involves two spatial dimensions and one temporal dimension. It might be useful to think in terms of 4vectors. Consider a pulse of light from the laser. Define two events to be the locations of the laser pulse at different times. Assume that a photon from the laser was emitted at the spacetime point ( t = 0 , x = 0 , y = 0) in the (moving) S reference frame. This corresponds to ( t = 0 , x = 0 , y = 0) in the observers frame S . Then this photon was registered at the spacetime point t = T , x = cT cos , y = cT sin . Using Lorentz transformation, we get the spacetime coordinates of this event (registration of the photon) in the S frame as t = ( t + vx /c 2 ) = T (1 + cos ) , x = ( x + vt ) = cT (cos + ) , y = y = cT sin ....
View
Full
Document
This note was uploaded on 11/05/2011 for the course PHY 105 at Princeton.
 '08
 LYMANA.PAGE
 Physics, mechanics

Click to edit the document details