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Question

If a speed moves away from you at half the speed of light and fires a rocket away from you at half the speed of light relative to the spaceship, common sense may tell you the rocket moves at the speed of light relative to you. But it doesn’t! The relativistic addition of velocities is given by$V = \frac { v _ { 1 } + v _ { 2 } } { 1 + \frac { v _ { 1 } v _ { 2 } } { c ^ { 2 } } }$Substitute 0.5c for both$v_1$and$v_2$and show that the velocity V of the rocket relative to you is 0.8c.

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$\textbf{Introduction:}$

The relativistic addition of the velocities is given by the formula:

$\begin{gather} V = \dfrac{v_1 + v_2}{1 + \dfrac{v_1v_2}{c^2}} \end{gather}$

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