Spaceship I, which contains students taking a physics exam, approaches Earth wit
ID: 2242389 • Letter: S
Question
Spaceship I, which contains students taking a physics exam, approaches Earth with a speed of 0.760 c, while spaceship II, which contains instructors proctoring the exam, moves away from Earth at 0.260 c, as in Figure P26.27. If the instructors in spaceship II stop the exam after 45 min have passed on their clock, how long does the exam last as measured by (a) the students?
(b) How long does the exam last as measured by an observer on Earth?
Explanation / Answer
As
Relative velocities add like relative velocity = (v1-v2)/(1-v1v2/c^2)
= (-0.760+0.260)c/(1 - (0.760*0.260))
= - 0.623c
Required time = time/sqrt(1 - relative time^2/c^2)
= 45/sqrt(1 - 0.623^2)
= 57.52 min
exam last as measured by an observer on Earth = time/sqrt(1 - v^2/c^2)
= 45/sqrt(1 - 0.260^2)
= 46.6 min
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