Question

thanks for the help with the first problem this is the last problem I have a question on...

A superball rebounds half the height it drops. The ball is dropped from a height of 176 feet. How far off the ground is the ball when it has traveled a total of 500 feet?

Answer 1

You do not say if you know about geometric series so with brute force:
It goes down 176 feet and bounces
total = 176
The first bounce up is 176/2 = 88 feet
total = 264
Then it also goes down 88 feet
total =352
then up 44
total = 396
then down 44
total = 440
then up 22
total = 462
then down 22
total = 484
then up 11
total = 495 when it is 11 feet high
then down 5 to reach 500
Leaving it 6 feet high.