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Question

# Pretend that the starship Enterprise in the previous problem is somehow traveling at $c$ with respect to the Earth, and it fires a drone forward at speed $c$ with respect to itself. Use the equation for the relativistic addition of velocities to show that the speed of the drone with respect to the Earth is still $c$.

Solution

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Again, to determine the drone's speed relative to Earth, we will use relativistic formula for relativistic addition of speeds:

$v=\dfrac{v_E+v_d}{1+\dfrac{v_E v_d}{c^2}}$

Where $v$ is speed of drone relative to the Earth and $c$ is speed of light.

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