27_InstSolManual_PDF_Part4

27_InstSolManual_PDF_Part4 - S be a frame attached to...

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27.17. Set Up: Let the frame attached to Arrakis be S and let the frame attached to the imperial spaceship be Let the positive x direction for both frames be from the spaceship toward Arrakis. Then and we want to solve for u . Solve: gives The speed of the starship rela- tive to Arrakis is 0.837 c . Since and the direction from the spaceship toward Arrakis is positive, the spaceship is moving away from Arrakis. Reflect: The Galilean transformation gives that the spaceship is moving away from Arrakis with a speed of The Lorentz transformation gives a larger speed. 27.18. Set Up: Let S be the laboratory frame and let be the frame of one of the particles, as shown in Fig- ure 27.18. Let the positive x direction for both frames be from particle 1 to particle 2. In the lab frame particle 1 is moving in the direction and particle 2 is moving in the direction. Then and is the velocity of particle 2 relative to particle 1. Figure 27.18 Solve: The speed of particle 2 relative to parti- cle 1 is 0.9988 c . shows particle 2 is moving toward particle 1. 27.19. Set Up: Let
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Unformatted text preview: S be a frame attached to planet Tatooine and let be a frame attached to the pursuit ship. Let the positive x direction for both frames be from the planet toward the pursuit ship. Then and is the velocity of the cruiser relative to the pursuit ship. Solve: means that the cruiser is moving toward the pursuit ship. Reflect: The Galilean transformation gives that the cruiser is moving toward the pursuit ship with a speed of The Lorentz transformation gives a larger speed. 0.800 c 2 0.600 c 5 0.200 c . v r , v r 5 v 2 u 1 2 u v / c 2 5 0.600 c 2 0.800 c 1 2 1 0.800 c 21 0.600 c 2 / c 2 5 2 0.385 c . v r 1 0.600 c . v 5 u 5 1 0.800 c S r v r , v r 5 v 2 u 1 2 u v / c 2 5 2 0.9520 c 2 0.9520 c 1 2 1 0.9520 c 21 2 0.9520 c 2 / c 2 5 2 0.9988 c . x r y r x y S S r 2 1 v r v 5 2 0.9520 c . u 5 0.9520 c 2 x 1 x S r 0.920 c 2 0.360 c 5 0.560 c . u , u 5 v 2 v r 1 2 vv r / c 2 5 0.360 c 2 0.920 c 1 2 1 0.360 21 0.920 2 5 2 0.837 c . v r 5 v 2 u 1 2 u v / c 2 v 5 1 0.360 c v r 5 1 0.920 c , S r . 27-4 Chapter 27...
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