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Spaceship I, which contains students taking a physics exam, approaches Earth with a speed of 0.60c, while spaceship II, which contains instructors proctoring the exam, moves at 0.28c (relative to Earth) directly toward the students. If the instructors in spaceship II stop the exam after 50 min have passed on their clock, how long does the exam last as measured by (a) the students (b) An observer on the Earth?

Respuesta :

Answer:

Let β = v / c          

proper time Δt'  is measured in a frame at the same place in a given frame - the proper time is measured in spaceship II moving at .28 c

a) spaceship I is moving at (.6 - .28) c = .32 c relative to proper time

Δt = Δt' / (1 - β^2)^1/2      as measured by students in ship I

Δt = 50 / (1 - .32^2)^1/2 = 52.8 m        measured by students

b) Δt = 50 / (1 - .28^2)^1/2 = 52.1 min  time elapsed for observer on earth

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