A ball is dropped
520 feet from the roof of a building. Suppose that with each bounce, the
ball goes up exactly x percent of its previous height. A man sitting
at his desk on the second floor at a height of 15 feet above the ground, sees the ball pass him 17 times. Find x.
(Source: Mathematics Teaching in the Middle School, Feb 1999).
I am trying to find the percent
of height that the ball goes up with each bounce.
Solve/Investigate the Problem
I must admit that I really did
not think in terms of proportions, but in terms of exponents and
logarithms. But when I solved, I did have to divide, and percents are
a form of a ratio.
of the Problem
Initially, the ball was dropped from
a height of 520 feet. With each drop the height of the ball decreased
x%. Cornell was sitting at his desk at work, and was RIDICULOUSLY off
task! (Well he was if he counted the number of bounces - what a lame!)
Since I have just been teaching
about exponents, I recognized that this could be done using exponents
520*x*x ft = 520x2 ft
520*x*x*x ft = 520x3ft
520*x*x*x*x ft = 520x4ft
And so on
drop 520x16ft = 15
So I got that x≈80.13%
Extensions of the Problem
Discuss possible extensions for
the problem and explore/investigate at least one of the extensions you
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