27.4. Set Up: The astronaut in the spaceship measures the proper time, since the end of a swing occurs at the same location in his frame. Solve: (a) (b) 27.5. Set Up: The instruments in the scram jet measure the proper time. The speed of sound is about Solve: and the time dilation effects are very small. 27.6. Set Up: The average lifetime measured in the pion frame is the proper time; Solve: (a) gives (b) 27.7. Set Up: The proper time is measured in the frame where the two events occur at the same point. Solve: (a) The time of 12.0 ms measured by the first officer on the craft is the proper time. (b) gives Reflect: The observer at rest with respect to the searchlight measures a much shorter duration for the event. 27.8. Set Up: The problem asks for u such that Solve: gives Jet planes fly at less than ten times the speed of sound, less than about Jet planes fly at much lower speeds than we calculated for u . 27.9. Set Up:
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