Spaceship I, which contains students taking a physics exam, approaches Earth wit

Question

Spaceship I, which contains students taking a physics exam, approaches Earth with a speed of 0.665 c, while spaceship II, which contains instructors proctoring the exam, moves away from Earth at 0.250 c, as in Figure P26.27. If the instructors in spaceship II stop the exam after 70 min have passed on their clock, how long does the exam last as measured by (a) the students?

How long does the exam last as measured by an observer on Earth?

Spaceship I, which contains students taking a physics exam, approaches Earth with a speed of 0.665 c, while spaceship II, which contains instructors proctoring the exam, moves away from Earth at 0.250 c, as in Figure P26.27. If the instructors in spaceship II stop the exam after 70 min have passed on their clock, how long does the exam last as measured by (a) the students? How long does the exam last as measured by an observer on Earth?

Explanation / Answer

the velocity of students as viewed by professor is

V' =(V-U)/[1-VU/c^2]

V' =(-0.665c-0.25c)/[1-(-0.665c)(0.25c)/c^2]

V'=-0.784c

r =gamma

r=1/sqrt[1-(V'/c)^2] =1/sqrt[1-(-0.784)^2]

r=0.786

so

t= r*to =0.786*70

t =55 min

b)

the velocity of earth viewed by professor is -0.25c

V=-0.25c

r =1/sqrt[1-0.25^2] =1.0327

t=1.0356*70 =72.29 min

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