Question:

Two identical particles of mass $m$ approach each other at equal and opposite speeds, $v$. The collision is completely inelastic and results in a single particle at rest. What is the mass of the new particle? How much energy was lost in the collision? How much kinetic energy was lost in this collision?

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer:

$M = \dfrac{2m}{\sqrt{1-\dfrac{v^2}{c^2}}}$

no energy is lost.

$\textrm{KE}_{lost} = 2mc^2 \left ( \dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}} - 1 \right )$