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Exercise:
Show that for non-relativistic velocities the classical addition formula Galilei is a good approximation.

Solution:
The relativistic expression for the velocity addition is u fracv+u'+fracvu'c^ For v ll c and u' ll c the denominator can be approximated as +fracvu'c^ & approx It follows that in this approximation velocities can be added using the expression u & approx v + u' This is the standard expression used in classical mechanics.
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Exercise:
Show that for non-relativistic velocities the classical addition formula Galilei is a good approximation.

Solution:
The relativistic expression for the velocity addition is u fracv+u'+fracvu'c^ For v ll c and u' ll c the denominator can be approximated as +fracvu'c^ & approx It follows that in this approximation velocities can be added using the expression u & approx v + u' This is the standard expression used in classical mechanics.
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special relativity
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velocity addition
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(1, default)
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ENG (English)
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