Question

Need help with this word problem, how am i supposed to know when it's at rest? wouldn't that be an infinite series?

suppose that a superball dropped from a height of 28 ft always rebounds 1/4 of the distance fallen. approximately how far does the ball travel before coming to rest?

Answer 1

It's called convergence.

\(28 + 28*.5 + 28*.5^2 + 28*.5^3 + ... = \dfrac{28}{1-0.5}\)

Answer 2

\[S \infty=37\]

Answer 3

so the answer is 37?

Answer 4

or double? 74

Answer 5

That may have been a little sloppy. Let's give it a better look. For you, please quit guessing. Let's get the right answer and stop using your shotgun.

Drops 28
Bounce #1: Rebounds 7 (28/4) and drops 7, thus it travels 14 = 28*.5 on the 1st bounce
Bounce #2: Rebounds 7/4 and drops 7/4, thus, it travels 7/2 = 28*.5*.5*.5 = 28*.5^3
Bounce #3: Rebounds 7/16 and drops 7/16, thus, it travels 7/8 = 28*.5*.5*.5*.5*.5 = 28*.5^5

Okay, I thin I get it. I was not quite correct up above.

\(28 + 28*.5 + 28*.5^3 + 28*.5^5 + 28*.5^7 + ...\)

A little algebra:

\(28 + 28*.5(1 + .5^2 + .5^4 + .5^6 + ...)\)

A little more:

\(28 + 14(1 + .5^2 + .5^4 + .5^6 + ...)\)

Two things.
1) Can you follow all that?
2) Can you add up the geometric series in the parentheses?

Don't be jumping all over the place. Just answer the questions.

Answer 6

\[s \infty=\frac{ a _{1} }{ 1-r }\] for \[a _{1}\]7 is \[\frac{7 }{ 1-.25 }\] or \[\frac{ 28 }{ 3 }\]times 2 plus 28... 46.67ft

Answer 7

Text makes you appear very condescending... but thank you for the help! :)

Answer 8

Text does not make me appear condescending. You may read however you wish. You were jumping all over the place and I told you not to do that. It's called honest. It is often mistaken for condescending.

Answer 9

Tone is hard to read I suppose. Either way, thanks for your help!

Answer 10

Tone is very hard to read. Thank you for responing to my explanation with open-mindedness.

Answer 11

You're a good teacher, it wasn't too difficult to follow your instruction. I appreciate it.