Complete Revised Edition Full.
, 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
1
Complete Revised Edition Full.
, Chapter 1 ! Relativity I
(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
2
Complete Revised Edition Full.
, Chapter 1 ! Relativity I
(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 2nd postulate.
(d) No. The result depends on the relative motion of the frames.
(e) No. The result depends on the speeds involved.
(f) Yes. Result is independent of motion.
(g) Yes. The charge is an intrinsic property of the electron, a fundamental constant.
1-9. The wave from the front travels 500 m at speed and the wave from the rear
travels at . As seen in Figure 1-15, the travel time is longer for the wave from the
rear.
3
Complete Revised Edition Full.
, 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
1
Complete Revised Edition Full.
, Chapter 1 ! Relativity I
(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
2
Complete Revised Edition Full.
, Chapter 1 ! Relativity I
(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 2nd postulate.
(d) No. The result depends on the relative motion of the frames.
(e) No. The result depends on the speeds involved.
(f) Yes. Result is independent of motion.
(g) Yes. The charge is an intrinsic property of the electron, a fundamental constant.
1-9. The wave from the front travels 500 m at speed and the wave from the rear
travels at . As seen in Figure 1-15, the travel time is longer for the wave from the
rear.
3
Complete Revised Edition Full.
