Question

A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance traveled by the ball.

Answer 1

I got 152.421 feet, but I just want to make sure I did it right

Answer 2

16 + 2(16*.81 + 16*.81*.81+...)
It's a GP

Answer 3

an = .81 a(n-1)

an = a0 * .81^n or some such

Answer 4

geometric progression, yes

Answer 5

Lol, thanks I got confused over its name. Geometric for an algebraic series sounds weird.

Does anyone here knows why it's called Geometric Progression?

Answer 6

\[16 + 32(\frac{81}{100})\sum_{0}^{\infty}(\frac{81}{100})\]

right?

Answer 7

geometric stuff tends to be multiplications; like finding the area of a square

Answer 8

\[16 + 32(\frac{81}{100})\sum_{0}^{\infty}(\frac{81}{100})^n\]

I mean

Answer 9

16 + 16*.81 + 16*.81 + 16*.81^2+ ...

16 + 2(16*.81 + 16*.81^2+ 16*.81^3+...)

\[16+2(16\frac{1-.81^{inf}}{1-.81})\]

Answer 10

the top tends to bow out to 1 i beleive

Answer 11

\[16+\frac{32}{.19}\]maybe?

Answer 12

I was thinking\[16+32\sum_{n=1}^{\infty}(0.81)^n=16+32[-1+\sum_{n=0}^{\infty}(0.81)^n]\]\[=-16+\frac{32}{1-0.81}\]because we have to strip out a term, no?

Answer 13

might have to factor out the .81 as well to get the first term to 1

Answer 14

amistre your answer is 32 off from mine, and turingtest, that's what i got :)

Answer 15

\[16+\frac{32*.81}{.19}\]is my gut feeling in the end :)

Answer 16

152.42.... yeah :)

Answer 17

\[(1+r+r^2+r^3+...)=\frac{1}{1-r}\]
since we had a 16*.81 at the start we need to factor it out to get this format; and then add in the original 16 that it fell from