Math help for another question on sequences and series, general applications

[Mandynguyennmm]

hi,

can i please have help for this question:

An elastic string drops down 60 cm and then bounces back
to 2/3 of its initial height. It keeps
bouncing, each time rising back
to 2/3 of its previous height. What
is the total distance through which the string travels?

thanks

[RuiAce]

This is almost the exact same as your earlier question, so I will not go into great depth. The difference is that it bounces down once more than it comes back up. (Earlier with the zig-zags you had two of the exact same GP's, whereas here one of them is essentially "one behind the other".)

So you have \(\left(60 + 40 + \frac{80}{3} + \frac{160}{9}\right) + \left(40 + \frac{80}{3} + \frac{160}{9} \right)\) which becomes \( \frac{60}{1 - \frac23} + \frac{40}{1 - \frac23} \)

Alternately, it's also equal to \( 60 + 2\times \frac{40}{1 - \frac23}\), by analysing the question a different way. I will leave that as your exercise. (Both of them will lead to the same answer.)

[Mandynguyennmm]

ohh i see, thanks

[Never.Give.Up]

This is almost the exact same as your earlier question, so I will not go into great depth. The difference is that it bounces down once more than it comes back up. (Earlier with the zig-zags you had two of the exact same GP's, whereas here one of them is essentially "one behind the other".)

So you have \(\left(60 + 40 + \frac{80}{3} + \frac{160}{9}\right) + \left(40 + \frac{80}{3} + \frac{160}{9} \right)\) which becomes \( \frac{60}{1 - \frac23} + \frac{40}{1 - \frac23} \)

Alternately, it's also equal to \( 60 + 2\times \frac{40}{1 - \frac23}\), by analysing the question a different way. I will leave that as your exercise. (Both of them will lead to the same answer.)

Hey Rui
I'm having difficulty with this question too 
sorry im dumb...but could you please explain your working..i don't really get it (like, where all your numbers are coming from)
thanks so much!

[RuiAce]

[Mandynguyennmm]

Hi,

i think the method you showed earlier is right, because it equals 300cm (the answer) .

This is because when the elastic string drops down it "bounces back" up and "keeps bouncing", each time rising back to 2/3 of its previous height (so it is like a ball?)

thanks

[RuiAce]

Yeah right. I confused myself. The original answer is fine.

I'll draw a diagram for this in a bit. Edit:



(I must have been cooked a few moments ago.)

[Never.Give.Up]

Yeah right. I confused myself. The original answer is fine.

I'll draw a diagram for this in a bit. Edit:

(Image removed from quote.)

(I must have been cooked a few moments ago.)

ummm...for some reason i can't see this...
but because 40 is 2/3 60 it = a...what i was wondering then was why do you add 60 (u obv. x2 because its bouncing back up? do u just add the 60cm because it drops down 60cm before bouncing back 40cm...?)

EDIT:
All good sorry dont worry...think i've got it (wasnt thinking straight for a minute there!)
thanks anyways