coefficient of restitution
The coefficient of restitution is a single number, written e, that says how bouncy a collision is. Drop a ball and watch how high it comes back: a lively superball nearly returns to your hand (bouncy, e near 1), while a beanbag just flops (dead, e near 0). The coefficient captures that whole spectrum in one figure between 0 and 1.
Precisely, e is the ratio of the relative speed of separation to the relative speed of approach: e = (speed the objects move apart after) / (speed they came together before). e = 1 is a perfectly elastic collision (they separate as fast as they met, no kinetic energy lost); e = 0 is a perfectly inelastic collision (they do not separate at all — they stick). Everything in between is a partially inelastic collision. For a ball bouncing off a fixed floor, e equals the square root of the rebound height divided by the drop height, e = sqrt(h_bounce / h_drop).
Engineers and sports bodies care about e a great deal: it sets how far a golf ball flies off a driver, how a basketball bounces, how safe a car bumper is. It is a handy shortcut precisely because it summarizes the messy energy loss of a collision in one measurable number, without needing to track every force.
A basketball dropped from 1.8 m rebounds to 1.2 m. Then e = sqrt(1.2 / 1.8) = sqrt(0.667) = about 0.82. It came back to two-thirds of its height, but only 82% of its speed — because kinetic energy scales with v^2, and about a third of that energy was lost to the bounce.
Rebound height gives e directly; e itself is a speed ratio, not a height ratio.
The coefficient of restitution is defined by relative speeds, not by heights or energies directly. e = 1 means kinetic energy is conserved (elastic); e = 0 means the objects stick (perfectly inelastic). It is a property of the pair and the impact, not a fixed property of one material alone.