Problem B

Boing! Boing! Boing!

A Superbball is a special kind of ball that will always bounce to half of the height from which it fell. Supposing that it is dropped from a building that is \(128\,\)m tall, answer the following questions.

How high will it bounce after it hits the ground for the third time?

How many times must the ball hit the ground so that the next bounce has a height of \(2\,\)m?

How many times must the ball hit the ground so that the next bounce has a height of \(25\,\)cm?

How tall would a building have to be if, after hitting the ground ten times, the ball bounces to \(1\,\)m? Is there a building this tall?

Extension: Test different balls to see how high they bounce when dropped from \(1\,\)m.

**Themes:** Number Sense, Algebra