Question

math question: Find the total vertical distance traveled (counting up and down both as positive distances) of a ball dropped from a height h and, after each bounce, bouncing back to r times the height reached on the previous bounce.

Answer 1

careful with this one

Answer 2

i never got this thing..isnt it just infinite geometric thingy?

Answer 3

yes, but not until after the first drop

Answer 4

this is a converging series - yes geometric with common ratio < 1

Answer 5

right satellite

Answer 6

so put that aside, because it is not part of the geometric series, that is what is usually so confusing
add the initial "h" at the end

Answer 7

r<1

Answer 8

There are several ways to do the bouncing ball question. One way to do it is form a geometric series of the ball going down. If you start at 100 feet and it comes back up 1/2 the way, find the sum of the series.
100, 50, 25, ...
\[S_{n} = \frac{a_{1}}{1 - r}\]\[S_{n} = 200\]Now, that is the distance going down.
Double it to get the distance going up. 400. However, you didn't go up that distance at the start, but rather started there.
Subtract \(a_{1}\) in order to get the answer.
400 - 100 = 300