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Chapter 37: Q27P (page 1147)
A particle moves along the x' axis of frame S' with velocity 0.40c. Frame S' moves with velocity 0.60c with respect to frame S. What is the velocity of the particle with respect to frame S?
The velocity of the particle with respect to frame S is 0.81c.
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A meter stick in frame makes an angle of with the x鈥� axis. If that frame moves parallel to the x-axis of frame with speed 0.90c relative to frame , what is the length of the stick as measured from S ?
Stellar system Q1 moves away from us at a speed of 0.800c. Stellar system Q2, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q2 as measured by an observer in the reference frame of Q1?
Superluminal jets. Figure 37-29a shows the path taken by a knot in a jet of ionized gas that has been expelled from a galaxy. The knot travels at constant velocity at angle from the direction of Earth. The knot occasionally emits a burst of light, which is eventually detected on Earth. Two bursts are indicated in Fig. 37-29a, separated by time as measured in a stationary frame near the bursts. The bursts are shown in Fig. 37-29b as if they were photographed on the same piece of film, first when light from burst 1 arrived on Earth and then later when light from burst 2 arrived. The apparent distance traveled by the knot between the two bursts is the distance across an Earth-observer鈥檚 view of the knot鈥檚 path. The apparent time between the bursts is the difference in the arrival times of the light from them. The apparent speed of the knot is then . In terms of , , and , what are (a) and (b) ? (c) Evaluate for and . When superluminal (faster than light) jets were first observed, they seemed to defy special relativity鈥攁t least until the correct geometry (Fig. 37-29a) was understood.
The plane of clocks and measuring rods in Fig. 37-19 is like that in Fig. 37-3. The clocks along the x axis are separated (center to center) by 1light-second, as are the clocks along the y axis, and all the clocks are synchronized via the procedure described in Module 37-1. When the initial synchronizing signal of t = 0 from the origin reaches (a) clock A, (b) clock B, and (c) clock C, what initial time is then set on those clocks? An event occurs at clock A when it reads 10 s. (d) how long does the signal of that event take to travel to an observer stationed at the origin? (e) What time does that observer assign to the event?
The length of a spaceship is measured to be exactly half its rest length. (a) To three significant figures, what is the speed parameter of the spaceship relative to the observer鈥檚 frame? (b) By what factor do the spaceship鈥檚 clocks run slow relative to clocks in the observer鈥檚 frame?
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