Sequences and Series help? (1 Viewer)

[Jayjays332211]

A ball has the property that when it falls from a height h to the ground it rebounds to a height of 2/3h. If a ball is dropped from a height of 9m, find:

a) How far has it travelled altogether by the time it hits the ground for the fourth time?

b) Theoretically, how far will it travel before coming to a rest?

Been trying to work at it all day, just a bit of help in the right direction would be nice.
With question a) I know that the answer should be 34.33 (I added 9+6+6+4+4+2.67+2.67) but when I put in the formula of Sn= a(1-r^n)/1-r I dont get the right answer -.-

 

[barbernator]

a) although this is a geometric progression, for this part it is easies to do this I added 9+6+6+4+4+2.67+2.67 like you did. The way to put it into the formula is to take a=9, r=2/3 n=4. Multiply this answer by 2, and then subtract 9. This is because in the motion it moves up and down, doubling the distance, yet 9m is only repeated once as it starts from that height.

b) Taking n-->infinity, a/1-r=27. This is for all the instances when the ball is falling downwards. As before, multiply by 2 and subtract 9 to get the overall distance being 45m

 

[Jayjays332211]

When I place it into the formula though, I get 2.926 (Before multiplying it by 2 and subtracting 9)

 

[barbernator]

<a href="http://www.codecogs.com/eqnedit.php?latex=\frac{9(1-(2/3)^{4})}{1/3}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{9(1-(2/3)^{4})}{1/3}" title="\frac{9(1-(2/3)^{4})}{1/3}" /></a>