# How many bounces will the ball take?

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Donald Duck throws a ball from a 90 feet building. The ball is quite bouncy and when it hits the ground, it bounces back half way up. It keeps bouncing back to half way up.

How many bounces will the ball take before it comes to a permanent halt?

SherlockHolmes Expert Asked on 23rd October 2015 in

This depends on the definition of “a bounce”.

In order for anything to bounce, it must first absorb energy and then release the energy.  Basically, the energy is temporarily stored in the distortion of the object, and then released when the object “springs” back to its original shape.  The deformation of the ball causes the ball to compress.  The ball can be considered to have stopped bouncing when the energy released by springing back is less than the amount of energy required to lift the ball by a distance equal to its compression.  When the energy released reaches that point, the ball is at rest.

Unfortunately, nothing in the question allows us to determine how much the ball deforms when it bounces, thus the number of bounces can’t be determined.  The answer is most certainly not “infinite“, which is the naive answer you get from considering the geometric sequence of a “perfect” ball that doesn’t compress at all when it bounces.

dougbell Genius Answered on 24th October 2015.

The ball will make infinite bounces before it is stopped.
As per the puzzle it will keep on bouncing half way up every time it hits the ground. But gravity will play its part at certain point of time which will make it stop.

SherlockHolmes Expert Answered on 24th October 2015.

What is “halfway”? One logical assumption is the midpoint of the ball. In that case once halfway is less than the radius of the ball, it is at rest.

on 24th October 2015.

Besides, eventually you reach the Plank length (after around 120 bounces), which is indivisible.

on 24th October 2015.

There are not enough details to answer the question. The ball has a of course some weight. If converting 9o feet to millimeters  its 27432. If the ball weight is such that it can’t bunce less than 1mm and since 2^15=32768 so the answer will be up to 14 times at most

Moshe Expert Answered on 20th December 2022.

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