Spacecraft I, containing students taking a physics exam, approaches the Earth wi

Question

Spacecraft I, containing students taking a physics exam, approaches the Earth with a speed of 0.680c (relative to the Earth), while spacecraft II, containing professors proctoring the exam, moves at 0.220c (relative to the Earth) directly toward the students. The professors stop the exam after 46.0 min have passed on their clock.

(a) For what time interval does the exam last as measured by the students?___ min

(b) For what time interval does the exam last as measured by an observer on Earth? ____min

Explanation / Answer

Tp = time on professors clock = 46 min

Ts = time on students clock

Te = time on observers clock

V1 = 0.680c

V2 = - 0.220c        towards student

velocity of student' spacecraft relative to professor's spacecraft is given as

V12 = (V1 - V2) / (1 - V1V2/c2) = (0.680c - (-0.220c) ) / (1 - (0.680c)(-0.220c)/c2) = 0.900c / 1.1496 = 0.783c

time on students clock is given as

Ts = Tp / sqrt (1 - (V12/c)2) = 46 / sqrt (1 - (0.783c/c)2) = 73.95 min

b)

time on observers clock is given as

Te = Tp / sqrt (1 - (V2/c)2) = 46 / sqrt (1 - (0.220c/c)2) = 47.2 min

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