The height of the Leaning Tower of Pisa is 183.27 feet from the ground
on the low side and 185.93 feet on the high side.
If a ball is dropped from the low side of the tower, and on each rebound
the ball rises exactly seven-tenths of its previous height,
what distance
will it travel before it comes to rest? (Give an exact answer, not an approximation)
Solution to the Problem:
The answer is NOT 610.9 feet as I reported earlier, but actually 1,038.53 feet! Many thanks to Tom Laidlaw for correcting my mistake.The distance traveled going DOWN is 183.27 + .7(183.27) + .7(.7(183.27)) + .7(.7(.7(183.27))) + ...
You can use the formula for a geometric series: Sum = a / (1 - r)
In this problem, the sum = 183.27 / (1 - .7) = 183.27 / .3 = 610.9 feet, which represents ONLY the distances going DOWN.
But as Tom pointed out, I forgot to take into account the rebound (or the distances going back up.
So, you could set up another infinite series or you could just double the answer for going up and subtract the initial term of the series.
Hence, the TOTAL distance travelled is 2(610.9) - 183.27 = 1,038.53 feet.
Correctly solved by:
| 1. Tom Laidlaw | Vancouver, Washington |
| 2. James Alarie | Flint, Michigan |
| 3. Kimberly Howe | Vienna, Virginia |