The tower of Pisa

The old discussion about the intentional inclination or not of the Tower of Pisa becomes fashionable once in a while. Among scientists and mathematicians of speculation that was built in the twelfth century to be able to prove scientifically certain questions of gravitational attraction, but others say that the tower leans for a defect in the base.

In a book of photographs of the world of one Shebb, it is said that “it measures 50 feet in diameter and that it leans 30 feet perpendicularly. As the base did not become solid enough, it began to tilt before it was 1/3 of the whole built. "

All this not only does not match the information given to us by the assistant who accompanied us to the top of the tower, but is against common sense. It is also hard to believe that the architect was so papanatas to finish the tower knowing, when it was 1/3 built, that he was already bowing.

It is known that Galileo said that the tower was made that way for scientific reasons, and in fact it was there that he refuted the philosophy of his opponents that maintained that the speed of an object's fall is proportional to its weight.

But it is that long before Galileo, there was a problem, which is said to be one of those that motivated the construction of our beloved leaning tower of Pisa, whose answer I have not found in any mathematical work.

An elastic ball is pulled from the top of the tower, which measures exactly 179 feet. In each bounce will rise 1/10 of the height from which it fell. How far did the ball travel before remaining completely still?

Solution

The ball will rest after having traveled a distance of 218 feet, 9 inches and 1/3.

Some assume that the answer 218,777777+ would be more precise, but if the line of sevens were taken up to a billion decimals, it would not be as concrete as 9 inches and 1/3.