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# ch1 - Chapter 1 Relativity I 1-1 Once airborne the plane's...

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1 Chapter 1 ! Relativity I 1-1. Once airborne, the plane’s motion is relative to still air. In 10 min the air mass has moved toward the east. The north and up coordinates relative to the ground (and perpendicular to the wind direction) are unaffected. The 25 km point has moved 10.8 km east and is, after 10 min, at west of where the plane left the ground (0, 0, 0) after 10 min the plane is at (14.2 km, 16 km, 0.5 km). 1-2. (a) (b) From Equation 1-7 the correction (c) From experimental measurements No, the relativistic correction of order 10 ! 8 is three orders of magnitude smaller than the experimental uncertainty. 1-3. 1-4. (a) This is an exact analog of Example 1-3 with L = 12.5 m, c = 130 mph, and v = 20 mph. Calling the plane flying perpendicular to the wind #1 and the one flying

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Chapter 1 ! Relativity I 2 (Problem 1-4 continued) parallel to the wind #2, #1 will win by ) t where (b) Pilot #1 must use a heading relative to his course on both legs. Pilot #2 must use a heading of 0° relative to the course on both legs. 1-5. (a) In this case, the situation is analogous to Example 1-3 with L = , v = , and . If the flash occurs at t = 0, the interior is dark until t = 2 s at which time a bright circle of light reflected from the circumference of the great circle plane perpendicular to the direction of motion reaches the center, the circle splits in two, one moving toward the front and the other toward the rear, their radii decreasing to just a point when they reach the axis 10 ! 8 s after arrival of the first reflected light ring. Then the interior is again dark. (b) In the frame of the seated observer, the spherical wave expands outward at c in all directions. The interior is dark until t = 2s, at which time the spherical wave (that reflected from the inner surface at t = 1s) returns to the center showing the entire inner surface of the sphere in reflected light, following which the interior is again dark. 1-6. Yes, you will see your image and it will look as it does now. The reason is the second postulate: All observers have the same light speed. In particular, you and the mirror are in the same frame. Light reflects from you to the mirror at speed c relative to you and the mirror and reflects from the mirror back to you also at speed c , independent of your motion. 1-7. (Equation 1-12) Where
Chapter 1 ! Relativity I 3 (Problem 1-7 continued) 1-8. (a) No. Result depends on the relative motion of the frames. (b )No. Results will depend on the speed of the proton relative to the frames. (This answer anticipates a discussion in Chapter 2. If by "mass," the "rest mass" is implied, then the answer is "yes," because that is a fundamental property of protons.) (c) Yes. This is guaranteed by the 2 nd postulate.

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ch1 - Chapter 1 Relativity I 1-1 Once airborne the plane's...

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