Final answer:
The physical property being measured by the rebound of the basketball is the coefficient of restitution (e), which indicates the elasticity of the ball's collision with the floor.
Step-by-step explanation:
When a basketball referee releases the ball to check if it rebounds to about waist level, they are measuring the coefficient of restitution (e). This physical property indicates how elastic the collision is when the basketball hits the floor and bounces back up. The higher the coefficient of restitution, the less energy is lost in the bounce, meaning the ball is well inflated and suitable for play.
The coefficient of restitution is calculated using the ratio of the rebound height to the height from which the ball was dropped, square rooted (c = (h/H)¹/²). This experiment is similar to the take-home experiment where a tennis ball's bounce on a racquet is used to measure its coefficient of restitution.