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179. Problem 2.24 (R) Two spaceships, each of proper length 100 m, pass
near one another heading in opposite directions. If an astronaut at the front
one ship measures a time interval of
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for
the second ship to pass him, then (a) we have to find the relative
velocity of the spaceships; (b) the time interval measured on the first
spaceship for the front of the second spaceship to pass from the from the front
to the back of the first spaceship.|
Solution: Click For PDF Version Observations on the motion of the second spaceship are being made from the
first spaceship. Let the speed of the second spaceship as observed from the
first spaceship be
The proper length of each spaceship is 100 m. The length of the second spaceship measured by the first spaceship will be Lorentz contracted
The time for the second spaceship to pass the first spaceship is observed to
be
We have
And the relative velocity of the two spaceships is
(b) The time interval measured on the first spaceship for the front of the second spaceship to pass from the front to the back of the first spaceship will be its length divided by the speed with which the second spaceship is moving towards it. The length of the spaceship is 100 m. Therefore, the time taken will be
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.
. Thus we
have
