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Relativistic Physics

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A spaceship travels with a speed of 0.6 c as
it passes by the Earth on its way to a distant
star, as shown in the diagram below. The
pilot of the spaceship measures the length of
the moving ship as 10 m.
Determine its length as measured by a per-
son on Earth. Answer in units of m.

The pilot of the spaceship observes that the
spaceship travels for 2 years.
Determine how much time has passed ac-
cording to a person on Earth. Answer in units
of years.

Some time after passing the Earth, the pilot
shoots a laser pulse backward at a speed of
3 *10 ^8 m/s with respect to the spaceship.
Determine the speed of the laser pulse as
measured by a person on Earth.
Answer in units of m/s.

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Please see the attached file.

The length measured in a reference frame where the object is at rest will be the longest. In all other reference frames the length of the object will be measured as shorter.

Let L0 be the length of the object measured in its rest system:

And in the non-moving frame:

According to Lorentz' transformation:

Thus:

If the measurement of the two coordinates were taken simultaneously in the ...

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