Question

A pendulum is released and swings until it stops. If it passes through an arc of 35 inches the first pass, and if on each successive pass it travels 4/5 the distance of the preceding pass, how far will it travel before stopping?

Answer 1

possible answers are, 210,175,140, and 315

Answer 2

I think there isn't an answer since if it always travels 80% of the previous distance, then technically it should always be travelling

Answer 3

I tired taking the log of it but ended up having to take log 0, which is undefined

Answer 4

You wouldn't be doing anything close to that, it's a geometric series problem.

Answer 5

Aaa right I misread the question

Answer 6

Yeah you're right it should converge

Answer 7

that's right it's a geometric series problem, I'm just trying to figure out how to set it up

Answer 8

I'm just making sure I don't put down something stupid as an answer. Bit rusty.

Answer 9

It's multiple choice so I was going to just pick one.

Answer 10

Well the basic formula for a geometric series is \[Sn = \frac{ a1(1-r^n) }{ 1-r }\]

Answer 11

So all you need to do is insert the values into their places

Answer 12

So you start with 35 and then each pass is 35(4/5)^n. So you could have 35 + 35*sum (4/5)^n. You can use your geometric series formula of 1/(1-r) to see what (4/5)^n converges to from there. If you do that, 1/(1-(4/5)) = 5. So you end up 35 + 35(5) = 210

Answer 13

\[Sn = \frac{ 35(1-0.8^n) }{ 1-0.8 }\]

Answer 14

And then you have to solve for n

Answer 15

Here's how I set it up personally, maybe it'll look like something familiar, maybe not *draws*

Answer 16

Teinis that would give me 35

Answer 17

Nah I don't think it would

Answer 18

Because you can't just cancel 0ff the (1-0.8)