When the SuperBall® was introduced in the 1960’s, kids across the United States were amazed that these hard rubber balls could bounce to 90% of the height from which they were dropped.
a. If a SuperBall® is dropped from a height of 2m, how far does it travel by the time it hits the ground for the tenth time? (Hint: The ball goes down to the first bounce, then up and down thereafter.)

Question

When the SuperBall® was introduced in the 1960’s, kids across the United States were amazed that these hard rubber balls could bounce to 90% of the height from which they were dropped. 
a. If a SuperBall® is dropped from a height of 2m, how far does it travel by the time it hits the ground for the tenth time? (Hint: The ball goes down to the first bounce, then up and down thereafter.)

anonymous · Answer

I'm assuming this problem is asking for the height of its bounce after the 10th bounce? From the way its sounded, I'm not sure if its asking for the total distance covered by the time it hits the ground for the 10th time.

Assuming the first, It's a geometric sequence problem. So, ar^n=y, solving for y being the height. y=2(0.9)^10

Assuming the second,

$$\sum_{n=0}^{9}=a/1-r$$

It's summation to 9, because if you think about the first term. n=0, the distance travelled for the first time it hits the ground is 2. So it's one less than the bounce number. So, 2/0.1=20

anonymous · Answer

Oh for the second part, nevermind the a/1-r part, that's the formula for the summation to infinity. You want to use s=a(1-r^n)/1-r instead

anonymous · Answer

Ok wait I'm confused... I think it is asking the total distance covered by the time it hits the ground for the 10th time..... You kinda lost me sorry?

anonymous · Answer

So its just the summation of 2(0.9)^n from 0 to 9, so use the formula s=a(1-r^n)/1-r  i posted

anonymous · Answer

lol o wait pellet i forgot distance on the way up so I think you have to multiple your answer by 2 and subtract 10.. someone correct me if i'm wrong