# Relativistic Time and Length Dilation

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Two space ships each 100m long when measured at rest travel toward each other at a speed of .85c relative to earth.

a) How long is each ship as measured by someone on earth?

b) How fast is each ship traveling as measured by someone on the other ship?

c) How long is one ship when measured by an observer on the other?

d) At time t=0 on earth the fronts of both ships are together as they just begin to pass each other; at what time on earth are the ends together?

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This solution discusses relativistic time and length dilation.

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(a)

Relativistic contraction along the direction of motion is given by

dx = dx_0*sqrt(1-v^2/c^2)

where dx_0 = 100 m is the proper length (measured in the rest frame of a ship)

Therefore the length of a ship as measured on Earth is

L = 100m * sqrt( 1 - 0.85^2) = 52.6783 m

(b)

The ...

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