Sum sequence of a geometric series

[thekopite]

Homework Statement

A 'supa-ball' is dropped from a height of 1 metre onto a level table. It always rises to a height equal to 0.9 of the height from which it was dropped. How far does it travel in total until it stops bouncing?

Homework Equations

The Attempt at a Solution

The consecutive heights which the ball attains form a geometric series with first term a=1 and common ratio 0.9. Using the formula for the sum to infinity of the series, I am left with S = a/(1-r) = 1/0.1 = 10 metres
However, the answer given is 19 metres. I don't understand how to get to this answer, is this just a typo?

 

[Infinitum]

Hi thekopite! Welcome to PF

When the ball moves up 0.9h, it also comes down. You need to include that in your answer

 

[Millennial]

Hi thekopite! Welcome to PF

When the ball moves up 0.9h, it also comes down. You need to include that in your answer

Each bounce of the ball has an identical coming down length. For example, if the ball bounces 0.9 metres, it will also come down 0.9 metres, traveling a total distance of 1.8 metres.

 

[Infinitum]

Each bounce of the ball has an identical coming down length. For example, if the ball bounces 0.9 metres, it will also come down 0.9 metres, traveling a total distance of 1.8 metres.

Exactly...Except the first 1m fall Edit : Oops...I thought the OP posted.:uhh:

 

[thekopite]

thanks, i get it know. feeling a little dumb.