# Carnivals and Quadratics

## Introduction

A carnival game involves striking a lever that forces a weight up a tube. If the weight reaches the bell to ring it, then the contestant wins a prize. The height of the ball is effected by the starting height and velocity. Gravity pulls objects toward Earth at approximately 16 feet per second per second.

## Adjust the parameters to model each situation. Animate time to see the height of the ball.

If the starting height is 3 feet, the velocity is 32 feet per second, and the bell is at 20 feet, what is the maximum height and will a prize be won? If a prize won't be won, would raising the starting height by 1 foot make a difference?

With a bell height of 30 feet and starting height of 2 feet, what is the minimum velocity needed to reach the bell?

Does increasing the starting height be 1 foot or increasing the velocity by 1 foot per second have a greater effect on the maximum height?