Question

A superball dropped from a height of 40ft always rebounds 1/5 of the distance fallen. approximately how far does the ball travel before coming to rest? Please help :(

Answer 1

geometric series for this one
leave the initial drop of 40 out of it, we can put that in later

Answer 2

drops 40 put that aside
bounces up \(40\times \frac{1}{5}\) and down \(40\times \frac{1}{5}\) for a total of
\[80\times \frac{1}{5}\]

Answer 3

next one is
\[80\times( \frac{1}{5})^2\]

Answer 4

and so on
you have to add
\[80\times \frac{1}{5}+80\times (\frac{1}{5})^2+80\times (\frac{1}{5})^2+...\]

Answer 5

Do you know the final answer?

Answer 6

i can compute it, yes
does this summing a geometric series look familiar?

Answer 7

yes it's the section I'm on now

Answer 8

we can make life a little easier if we make it
\[20+20\times \frac{1}{5}+20\times (\frac{1}{5})^2+...\]

Answer 9

or even easier as
\[20(1+\frac{1}{5}+(\frac{1}{5})^2+(\frac{1}{5})^2+...\] formula for the second part is
\[\frac{1}{1-r}\] where \(r=\frac{1}{5}\)

Answer 10

you get
\[\frac{1}{1-\frac{1}{5}}=\frac{1}{\frac{4}{5}}=\frac{5}{4}\]
now multiply that by \(20\) then add that \(40\) for the first drop

Answer 11

\[20\times \frac{5}{4}=25\]if my arithmetic is correct, making your answer \(65\)

Answer 12

Thank you for your help, but unfortunately that was incorrect

Answer 13

really? maybe i made a mistake
we can try again if you like

Answer 14

lets go slow
it goes up \(40\times \frac{1}{5}\) and down \(40\times \frac{1}{5}\) for a total of
\[8+8=16\] oh damn

Answer 15

i said 20 and it was 16 because i cannot divide properly
lets try
\[16\times \frac{5}{4}=20\]

Answer 16

for a total of \(60\)