If a steel ball is dropped onto a steel floor from 1m how many bounces will it bounce if it rebounds to 90%?

Answer 1

Mathematically, an infinite number if it bounces up 90% every time. It never gets to zero. You need to set a threshold of what minimum percent you call a bounce.

Set a threshold like 1% to determine when it stops bouncing. Then solve 90% ^ n = 1%. n, the number of bounces to get to 1%, is the log of 1% over log 90% (log base 90% of 1% using crazy base log theorem)

This isn't an especially realistic model of how something bounces, but it will do for a problem.

edit: So I get 44 bounces. Using the 1mm threshold (as in the answer below) you should get 66 bounces. To get to where it stops making noise, you may well need another 20-30 bounces at least after that.

Answer 2

Bekki B cool start!
Intuitively you are on the right track

Try this one

k2=k1-k1/10=k1(1-1/10)
k3=k2-k2/10=k2(1-1/10)=k1(1-.9)(1-.9)
Or
k3=k1(1-.9)^n-1 or
k3=k(1-.9)^n or in general
kn=k(0.9)^n

k1...n is the amount in bounced the first time and n-th time

Then kn=k(0.9)^n
let kn=1mm
k=1m
ln(kn)=n ln(k(.9))

and
n=kn(kn)/ln(0.9k)
n=1 ln(.001)/(ln(.9 x 1)
correction
n=66