Distance related Series Question (Cal II)

[alingy1]

A ball bearing is dropped from a height of 8 meters onto a heavy metal plate. The
ball bounces each time to a height that is 107 of its preceding height. Assuming that the ball
continues to bounce indefinitely, find the total distance that it travels.


I did this:

Series:

SUM OF 8(7/10)^k from k=0..infinity. = a/(1-r)= 80/3 m.

Am I right?

 

[SammyS]

A ball bearing is dropped from a height of 8 meters onto a heavy metal plate. The
ball bounces each time to a height that is 107 of its preceding height. Assuming that the ball
continues to bounce indefinitely, find the total distance that it travels.


I did this:

Series:

SUM OF 8(7/10)^k from k=0..infinity. = a/(1-r)= 80/3 m.

Am I right?

Is that a typo?

Did you mean 7/10 of its previous height?

 

[HallsofIvy]

A ball bearing is dropped from a height of 8 meters onto a heavy metal plate. The
ball bounces each time to a height that is 107 of its preceding height.

From what you have below, I presume you mean 7/10 of its preceding height.

Assuming that the ball
continues to bounce indefinitely, find the total distance that it travels.


I did this:

Series:

SUM OF 8(7/10)^k from k=0..infinity. = a/(1-r)= 80/3 m.

Ok at the first few bounces. It goes down 8 m, then up 8(7/10) then down the same height so it has gone a total of 8+ 8(7/10)+ 8(7/10). It then goes up 8(7/10)(7/10)= 8(7/10)^2 and down 8(7/10)^2. You are missing the "up" portions of the trip.

Am I right?

Not quite.

 

[alingy1]

I meant 7/10

 

[alingy1]

Then:

(SUM OF 8(7/10)^k from k=0..infinity. = a/(1-r)= 80/3 m.)x2-8=45.33 m?

 

[alingy1]

Please do tell me if my answer is right.

 

[SammyS]

Then:

(SUM OF 8(7/10)^k from k=0..infinity. = a/(1-r) ≠ (80/3 m.)x2-8 ≈ 45.33 m?

To the left of the ≠ which I inserted is the total downward distance.

That result to the right looks good for the overall distance.