Answers to Chapter Three Questions

3.1) Anne and Bev have running synchronized watches with Bev standing L feet to the right of Anne. Anne notes the time that the front of the rogue bus passes her as T_front,Anne and the time that the rear of the rogue bus passes her, T_rear,Anne. Bev notes the time that the front of the bus passes her, T_front,Bev.

In terms of the data collected by Anne and Bev, the speed of the bus the distance the front of the bus moved in traveling from Anne to Bev, L, divided by the time it took the front of the bus to make the trip, T_front,Anne – T_front,Bev.

Once they know the speed of the bus, Anne can calculate the length of the bus because she knows how long it took the bus to pass by her, T_rear,Anne – Tf_ront,Anne. Multiplying that time difference by the speed of the bus gives the length of the bus.

3.2) The light flash takes 100 ns to go from Chuck to Dean. During that time the bus moves 60 feet. So Bev needs to be 160 feet to Anne’s right.

3.3) 160 feet

3.4) 200 feet

3.5) t_Chuck = 0, t_Ed = 0, t_Dean = 100 ns, t_Anne = 0, t_Bev,1 = 120 ns, and t_Bev,2 = 200 ns

3.6) I convinced myself!!

3.7)

3.8) A & B measure the speed of all light flashes to be 1 ft/ns. So the two flashes fired simultaneously when Chuck and Anne are adjacent travel through spacetime following identical worldlines.

3.9) Ed reaches Bev when her watch reads 120 ns. So traveled 120 ns times 0.6 ft/ns = 72 feet from the time the experiment began until he reached Bev. His starting position was X_Earth = 128 feet.

3.10) Yes, because 80% of the proper separation between Chuck and Ed, 160 feet, is exactly 128 feet.

3.11) It took the front of the bus 125 ns to cover 100 feet. Therefore the speed of the bus = 100/125 = 4/5 = 0.8 ft/ns. It took 150 ns for the bus to pass Anne so the length of the bus was 150 ns time 4/5 ft/ns = 120 feet.

3.12) According to Chuck, Bev traveled 160 ft at a speed of 3/5 ft/ns. Therefore it took Bev 800/3 ns to reach him.

3.13) According to Bev, Chuck had to travel 200 ft at 3/5 ft/ns to go from Anne to her. Since Anne’s watch read zero at the start of Chuck’s trip and Bev’s watch read 1000/3, A & B conclude that Chuck took 1000/3 ns to go from Anne to Bev. But when Chuck reached Bev, his watch read 800/3 ns or 80% of 1000/3 ns.

3.14) and 3.15) Ha! Ha!, the Principle of the Constancy of the Speed Light means observers on the red and blue buses measure exactly the same speed for the light flash, 1 ft/ns!