A spacecraft with a proper length of 350 m passes by an observer on the Earth. A
ID: 1508053 • Letter: A
Question
A spacecraft with a proper length of 350 m passes by an observer on the Earth. According to this observer, it takes 0.780 ps for the spacecraft to pass a fixed point. Determine the speed of the spacecraft as measured by the Earth-based observer. 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 0.200c (relative to the Earth) directly toward the students. The professors stop the exam after 74.0 min have passed on their clock. For what time interval does the exam last as measured by the students? For what time interval does the exam last as measured by an observer on Earth?Explanation / Answer
(6)
L = 350 m
t = 0.780 us
Let the speed as measured by observer be v.
L = Lo * sqrt(1 - v^2/c^2)
L = 350 * sqrt(1 - v^2/(3.0*10^8)^2)
Distance = Speed * time
350 * sqrt(1 - v^2/(3.0*10^8)^2) = v * 0.780 * 10^-6
v = 2.49 * 10^8 m/s
v = 0.83 c
(7)
(a)
The velocity of the students as viewed by professors is:
Relative speed of spacecraft II wrt Spacecraft I,
v = (- 0.680 - 0.20)/(1 + 0.68*0.20)
v = - 0.775 c
t = to/sqrt(1 - v^2/c^2)
t = 74.0/sqrt(1 - 0.775^2)
t = 117.1 min
(b)
Velocity of the earth as viewed by professors is = - 0.2 c
time interval measured by an observer on Earth = 74.0/ sqrt(1 - 0.2^2)
t = 75.52 min
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.