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.)

- anonymous

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- anonymous

is the answer 40/9?

- anonymous

no that doesnt work

- anonymous

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

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## More answers

- anonymous

Sorry I made a huge mistake. Im gonna correct it

- anonymous

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

- anonymous

ok

- anonymous

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

- anonymous

it still says its wrong...?

- anonymous

What is the correct answer?

- anonymous

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

- anonymous

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

- anonymous

What you mean by 17 8/9?

- anonymous

the answer is a mixed number

- anonymous

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

- anonymous

ok

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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)

- anonymous

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

- anonymous

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

- anonymous

I got 53/9

- anonymous

Convert 65/9 in a mixed number

- anonymous

53/9 works!

- anonymous

Convert 211/27 ins a mixed number too

- anonymous

What formula did you use?

- anonymous

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

- anonymous

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

- anonymous

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...

- anonymous

the= ball

- anonymous

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.

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Hey its cool man. I appreciate the help!

- anonymous

OK thanks. I like to help

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