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Naively, we would imagine that if a spaceship traveling at 
of the speed of light was to shoot a missile in the forward direction at 
of the speed of light (relative to the ship), then the missile would be traveling
at 
of the speed of light. However, Einstein's theory
of relativity tells us that this is too good to be true, because nothing can go faster than light. In fact, the relativistic equation for combining velocities in this way is not 
, but rather 
. In ordinary, everyday life, we never travel at speeds anywhere near the speed of light.
Show that the nonrelativistic result is recovered in the case where both 
and 
are infinitesimal.
of the speed of light was to shoot a missile in the forward direction at of the speed of light (relative to the ship), then the missile would be traveling
at of the speed of light. However, Einstein's theory
of relativity tells us that this is too good to be true, because nothing can go faster than light. In fact, the relativistic equation for combining velocities in this way is not , but rather . In ordinary, everyday life, we never travel at speeds anywhere near the speed of light.
Show that the nonrelativistic result is recovered in the case where both and are infinitesimal.
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