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 0.700c (relative to the Earth), while spacecraft II, containing professors proctoring the exam, moves at 0.200c (relative to the Earth) directly toward the students. The professors stop the exam after 78.0 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

(a)
The velocity of the students as viewed by professors is:

Relative speed of spacecraft II wrt Spacecraft I,
v = (- 0.7 - 0.20)/(1 + 0.7*0.20)
v = - 0.789 c

t = to/sqrt(1 - v^2/c^2)
t = 78.0/sqrt(1 - 0.789^2)
t = 126.95 min

(b)
Velocity of the earth as viewed by professors is = - 0.2 c
time interval measured by an observer on Earth = 78.0/ sqrt(1 - 0.2^2)
t = 79.60 min

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