Question

Have not the foggiest idea on how to complete this :(
A rubber ball dropped on a hard surface takes a sequence of bounces, each one 3/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled after it hits the surface the fifth time? Be sure to account for both drop and rebound distances.

Answer 1

well, thought i had it with this tl;dr
10 + ((10*(3/5))^1*2) + ((10*(3/5))^2*2) + ((10*(3/5))^3*2) + (10*(3/5))^4
but it isn't working, doesn't match my answer choices

Answer 2

All I've got are these choices and the answer to what I came up with is 1,822 which is obviously wrong.

Answer 3

if the ball bounces the next time 3/5 of the previous height
let's say the previous height is "a" what would be the height on the next bounce?

Answer 4

@jdoe0001 6

Answer 5

well, yes... notice it's just a geometric sequence, that has a 1st term of "10"
and we dunno the 5th term
but we know the "common ratio"

Answer 6

Is the common ratio 0.6?

Answer 7

yes

Answer 8

Now what do I do with that? :|

Answer 9

well, use the geometric sequence formula, which you surely have =)

Answer 10

I may have to look that up, my homework doesn't give it to me.

Answer 11

\(\large \bf a_{\color{red}{ n}}=a_1\cdot r^{{\color{red}{ n}}-1}\)

r= common ratio

Answer 12

a_n=10*0.6^5-1=-0.2224? That can't be right :c

Answer 13

AUGH I pulled a ditz move there, forgot the brackets *^-^
10*0.6^(5-1)=1.296

Answer 14

ahemm... ? so we know the common ratio say 3/5 so \(\large \bf a_{\color{red}{ n}}=a_1\cdot r^{{\color{red}{ n}}-1}\implies a_{\color{red}{ 5}}=10\cdot \left(\cfrac{3}{5}\right)^{{\color{red}{ 5}}-1}\)

Answer 15

And I'm still wrong because that isn't a choice either.

Answer 16

If this ball is dropped from a height of 10 feet,\(\bf \text{ what is the total vertical distance it has traveled}\) after it hits the surface the fifth time?

Answer 17

you're being asked for the sequence SUM, just like the in the previous exercise

Answer 18

oh, i pulled another ditz move on that one. i need to do what i tried to do the first time

Answer 19

give me a bit to try and do that

Answer 20

\[10+2(\frac{3}{5})(10)+2(\frac{3}{5})^2(10)+2(\frac{3}{5})^3(10)+2(\frac{3}{5})^4(10)\]

Answer 21

Is it B?

Answer 22

36 14/125

Answer 23

And yeah the equation you came up with was what I was doing pretty much.

Answer 24

well... what did you get?

Answer 25

notice Mertsj 's addition

Answer 26

10 + 2 (3/5) 10 + 2 (3/5)^2 10 + 2 (3/5)^3 10 + 2 (3/5)^4 10 = 36.112 = 36 14/125

Answer 27

\[10+12+7\frac{1}{5}+4\frac{8}{25}+2\frac{74}{125}=36\frac{14}{125}\]

Answer 28

Oh nvm, I see that it is correct. Thanks mates ;)
I dunno how I could repay you guys but I would pay if I could get help like this more often.