Question

This "real-life scenario" problem has me stumped... can anyone help me figure this out?

"A basketball is dropped from an original height of 9 ft. and on each bounce, bounces up 2/3 the distance it fell. How far will it have traveled by the time it hits the ground the fourth time?"

Answer 1

First off, when it asks how far it will have traveled... I don't understand whether it means horizontally or vertically.

Answer 2

do you know how to sum a geometric series?

Answer 3

oh nvm only says fourth bounce

Answer 4

So do I just find the sequence up to the fourth term and then find the sum of those?

Answer 5

down 9 (that is once)
up \(\frac{2}{3}\times 9=6\) and down 6 for a total of \(9+12=21\) that is twice

Answer 6

two more to go

Answer 7

up \(\frac{2}{3}\times 6=4\) and down \(4\)
now we are up to \(29\)

Answer 8

So then on the fourth bounce, it will go up about 2.67ft and then down about 2.67ft, which is a total of about 5.33, so altogether it traveled about 34.33ft by the time it hit the ground the fourth time

Answer 9

Is that right?