Quadratics and Sequences
Algebra
Modelling a bouncing ball.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Parabolic motion is the description of an object moving under the influence of gravity. What happens when a ball bounces? How long does it take to come to rest? Represent the bounce height in a table, a sequence, and a graph. Link limits and asymptotes.
Guiding Questions
- Drop a ball and let it bounce. What sequence do the bounce heights follow, and why?
- Measure bounce heights from a video. Is the sequence geometric? Find the common ratio for your ball.
- What total distance does the ball travel before it stops? Use your ratio and the formula for a geometric series.
- How does the ratio change with a different ball or surface, and can you connect height to a quadratic model of each bounce?