Question

A ball is dropped from a height of 3 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.
(a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter your answer as an improper fraction.)

Answer 1

is the answer 40/9?

Answer 2

no that doesnt work

Answer 3

This how I solved it:

Suppose K=1/3

first time d1=3
second time d2=3*K=1
Third time d3=1*k=1/3
Forth time d4=K(1/3)=1/9

Now adding up d1+d2+d3+d4, we get the total distance
d=40/9

Answer 4

Sorry I made a huge mistake. Im gonna correct it

Answer 5

That looks right to me but my online homework says its wrong...

Answer 6

ok

Answer 7

Suppose K=1/3

first time d1=3
second time d2=2*(3*K)=2
Third time d3=2*(2*k)=4/3
Forth time d4=2*K(4/3)=8/9

Now adding up d1+d2+d3+d4, we get the total distance d=65/9.

Is that correct. Hopefully yes

Answer 8

it still says its wrong...?

Answer 9

What is the correct answer?

Answer 10

IDK. in my book it gives a similar problem who's answer is 17 8/9

Answer 11

its the same problem only the ball is dropped from 9 feet instead of 3 ft

Answer 12

What you mean by 17 8/9?

Answer 13

the answer is a mixed number

Answer 14

Convert this number in a decimal number. Cannot remember how to do that!

Answer 15

ok

Answer 16

Is 17(8/9) the answer for the problem you have to solve? It doesnt make any sense!

Answer 17

no that was the answer to a similar problem. I thought if i gave you that answer then it might help you figure out the the problem

Answer 18

Yeah coz im trying to help you. Or are you challenging me?

Answer 19

A ball is dropped from a height of 9 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.
(a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. the answer to this is 17 (8/9)

Answer 20

But I need the answer for the problem your are solving now dude.

Answer 21

I dont know the answer to that one thats why im on here!

Answer 22

I got 53/9

Answer 23

Convert 65/9 in a mixed number

Answer 24

53/9 works!

Answer 25

Convert 211/27 ins a mixed number too

Answer 26

What formula did you use?

Answer 27

Can you write down step by step, how you got 53/9?

Answer 28

You start at 3

fall 3 rise (3 * 1.3) =1
fall 1 rise ( 1 * 1/3) = 1/3
fall 1/3 rise (1/3 * 1/3) = 1/9
fall 1/9

I stop at 1/9 because at fall 1/9 is the 4ht instant I hit the ground.

add 3 + 1 + 1 + 1/3 + 1/3 + 1/9 + 1/9
5+ 2/3 + 2/9
5 + 6/9 + 2/9
5 + 8/9
45/9 + 8/9
53/9

Answer 29

The formula of the the that is droped from 9 ft is 18-(1/3)^n-3. so i assume that the ball droped from 3ft had a similar formula...

Answer 30

the= ball

Answer 31

I can derive a formula but it will be hard since you start from the top and you want to know the distance it travels on the fourth hit to the floor.

Answer 32

ok thats cool. you got the answer right. Thanks!

Answer 33

btw the formula you use gives you 53/3 not 53/9 for the 4th hit.

Answer 34

Are you talking about the problem were the ball is droped from 9ft?

Answer 35

THe way I visualized it was right. However I made a mistake in fraction reduction. Sorry to dissapoint

Answer 36

Hey its cool man. I appreciate the help!

Answer 37

OK thanks. I like to help