# Question: a ball is thrown up 90 feet in the air...

###### Question details

A ball is thrown up 90 feet in the air. it comes down, bounces, and then rises up to a height of 81 feet. Then it falls to its second bounce, and so on. Each time it falls, it bounces back to 90% of its previous height.

(a) How high does the ball rise before the 30th bounce? (Please read the question carefully. If the question read “How high does the ball rise before the second bounce?” the answer would be 81 feet.)

(b) How far has the ball traveled when it hits the ground at the 30th bounce? (Again, read carefully. If the question read “How far has the ball traveled when it hits the ground at the second bounce?” the answer would be 90 feet up plus 90 feet down plus 81 feet up plus 81 feet down, for a total of 342 feet.)

(c) How far does the ball travel in the limit as the number of bounces approaches infinity?