How high a basketball will bounce on how hard you throw it at the
ground. If you drop a basketball without throwing it at the ground, it
will bounce back up to a fraction of its original height that is not
too far from 1.0 (0.75 is kind of typical for a well-inflated new
basketball). So if you drop a basketball from height of 20 feet, you
might expect it to go back up 15 feet or so. It will continue to
bounce, losing about a quarter of its height on each bounce.
If you threw the ball at the ground so that it hits the ground as
fast as it would had it been dropped from 20 feet, it will bounce back
to about 15 feet.
Now comes the hard part -- at what point will all this break down
and the basketball will not go any higher? This happens when some of
the energy of motion of the basketball is no longer available for the
bounce but goes into damaging the ball and/or the floor surface. For
very high bounces, air resistance also plays a role, but while it does
not limit the total height, it does reduce the bounce height. (there is
a limit from air resistance at which the ball goes fast enough to heat
up, but I suspect the first effect of the ball being damaged during the
bounce will happen at lower speeds than the air resistance problem).
During a bounce, the ball squishes against the floor and the air
inside pressurizes. When the air depressurizes and the ball unsquishes,
the ball springs up. The ball may squish so much that the rubber
bladder inside develops a tear. This is hard to do because basketballs
are reinforced with cloth and leather and/or rubber on the outside so
they do not tear. My guess is that if you shoot a basketball out of a
cannon at the ground at a suffiently high speed, the ball will tear
apart and stay on the ground. At what speed this happens depends quite
a lot on how the ball is made (and how old or worn it is, how well
inflated it is, etc.). My guess (and this is only a guess! I could be
very wrong on this!) is that you can get at least a few hundred feet in
a single bounce without destroying the ball, but it will be very very
hard to do this, not to mention dangerous! You don't want to get hit by
a basketball going that fast. And getting equipment to throw the
basketball that fast may be hard to make and dangerous to operate.
Dropping a basketball from a skyscraper could be an interesting
experiment but that experiment is not safe for people standing below,
and is certainly illegal.
Tom
(published on 10/22/2007)
