At the other end of the scale sits the perfectly elastic collision, where kinetic energy survives intact along with momentum. Two conservation laws pin both final velocities, and the algebra hands back $v_1 = \dfrac{(m_1 - m_2)u_1 + 2m_2u_2}{m_1 + m_2}$ for the first body — same cast as ever, $m_1, m_2$ in kilograms, $u_1, u_2$ the velocities before and $v_1$ the velocity of body 1 after, all in m/s. Learn the special case by heart: equal masses, target at rest, and they simply swap velocities — the striker stops dead. That is a Newton's cradle, and it is the anchor everything else is judged against.

Real collisions live in between, and the coefficient of restitution $e = \dfrac{v_2 - v_1}{u_1 - u_2}$ says where: the separation speed over the approach speed, a naked number with no units at all. $e = 1$ is perfectly elastic, $e = 0$ means they left together, and a dropped ball measures its own $e$ without a single velocity: $h_2 = e^2 h_1$, where $h_1$ is the drop height and $h_2$ the rebound height in the same unit. Why squared? Impact speed goes as $\sqrt{h}$, so a height ratio is a speed ratio squared. Forget that square and you will report a livelier ball than the lab ever bounced.