If you drop a ball from a height of 180 feet and it rises one tenth the height from which it fell each
time it bounces off the ground, what distance will the ball have travelled by the time it comes to rest?
: 220 feet.
: The ball travels 180 feet to begin with before hitting the ground. On the
first up and down
bounce, the ball will travel 2/10 of 180 feet (1/10 of 180 feet up and 1/10 of
180 feet down); then 2/100 of 180 feet; then 2/1000 of 180 feet and so forth. So after the initial 180
foot drop, the distance travelled is 2/10 + 2/100 + 2/1000 and so on which is the infinite decimal 0.222
(or 2/9) * 180 feet = 40 feet. Therefore the total distance travelled is 180 + 40 = 220 feet.
Do you have a suggestion
for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?