Mechanics, acceptable method?

1. Nov 24, 2013

BOAS

1. The problem statement, all variables and given/known data

A ball is dropped from rest from the top of a 6.10m building, falls straight down, collides inelastically with the ground and bounces back. The ball loses 10% of it's K.E every time it hits the ground. How many bounces can happen and the ball still reach a height of 2.44m above the ground.

2. Relevant equations

mgh = 1/2 mv2

xn = arn-1 (finding a term in a geometric series)

3. The attempt at a solution

I can come to an answer easily enough using the two equations stated above and the ideas of gravitational P.E being converted to K.E (so mass cancels out) and constructing a geometric series that uses r = 0.9 to accommodate the energy loss.

I have to essentially just guess terms until i'm in the right region and then increase or decrease my term until I reach the right answer. This seems somewhat messy to me, using trial and error.

Is there a cleaner method, that will use the information of the final height I need it to reach?

I'm just curious,

thanks!

2. Nov 24, 2013

Enigman

$x_n=ar^{n-1}$
$r^{n-1}=x_n/a$
$(n-1)logr=log x_n-loga$

3. Nov 24, 2013

BOAS

Ahh, thank you!

4. Nov 24, 2013

Staff: Mentor

$$x_n=x_0r^n$$ But, it's much easier just to do 1 bounce at a time. It couldn't take more than about 10 bounces with r = .9. Or, do it using: every two bounces is 0.81, every 3 bounces is 0.729.