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How high can a basketball bounce?

If we knew from what height the ball, when dropped, would reach its terminal velocity, and if we knew the percentage of rebound the ball would give, we could then be certain. I can only guess that a Basketball will rebound approximately 75% of the height from which it is dropped, and if the height at which it would reach terminal velocity is maybe 300 feet, the ball would bounce back up to 225 feet. Just a guess! A basketball has an elasticity (or "bounciness") of about 56 percent.
I'm not sure there's a theoretical limit. In practice, of course, there would be one: when the velocity of the ball impacting the ground is so great the ball explodes rather than bouncing. But you'd have to fire it out of some kind of basketball cannon to get it moving that fast.

The official standard for ball inflation is that the ball should bounce roughly 75% of its drop height (specifically, between 49" and 54") when dropped from 6 feet. If you're referring to just the height a dropped ball could bounce and you're not throwing it down with some kind of basketball-downward-hurling machine, you could calculate the theoretical bounce height by figuring out what terminal velocity is for a basketball, calculating how high you'd have to drop it from (assuming no atmosphere) to achieve that velocity, and then multiplying by 0.75. I'm not going to do it for you, because I'm not actually all that interested in the answer, but that's how you could do it if you are.

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