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.

Answer 1

a. Is this problem an example of a geometric series or an arithmetic series? Support your answer mathematically by applying the concepts from this unit.

b. 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.)

Answer 2

geometric because you multiply by .9 each time

Answer 3

the hint tells you not to start with 2 m, add that on at the end

Answer 4

all right, thanks, so is arithmetic only when you're adding or subtracting then?

Answer 5

yes

Answer 6

satellite where is the divisible by 11 problem?

Answer 7

i will repost it i can't find it. it actually asked for the remainder when you divide by 11, but the remainder is 0

Answer 8

all right, thanks satellite, the answer i got for part b. is .6972 meters

Answer 9

well that is not right for sure

Answer 10

it goes up
\[2\times .9\] and down
\[2\times .9\] and then up \[2\times .9^2\] and then down
\[2\times .9^2\] etc, you gotta add these up to the exponent of 10
then add 2 because it drops two meters to begin with

Answer 11

yeah i noticed my mistake, i think it is 2.915

Answer 12

well hold on. for one thing it goes up and down so don't forget to multiply by 2

Answer 13

the sequence is
\[4\times .9+4\times .9^2+4\times .9^3 + ... + 4\times .9^{10}\]

Answer 14

but that would be just the distance down every time, i guess i should multiply it by 2 to account for the ball's travel back up

Answer 15

right that is why i used 4

Answer 16

which is 5.83 meters total distance travelled

Answer 17

you could of course use 2 and then double the answer

Answer 18

i believe you. don't forget to add 2 at the end

Answer 19

oh yeah, almost forgot, thanks

Answer 20

did you use
\[4\times \frac{1-.9^{10}}{1-.9}\] or
\[4\times \frac{1-.9^{11}}{1-.9}\]? i always forget which one is rigtht

Answer 21

i did it a harder way because i didn't notice there was a simpler equation. i added 2 0.9 1.8 0.9 1.62 0.9 1.45 0.9 1.305 0.9 1.174 0.9 1.05 0.9 0.945 0.9 0.85 0.9 0.765 0.9, the spaces are where i multiplied obviously