# Analyzing the Motion of Soccer Ball using a Camera and Calculus

#### Posted March 13, 2013

#### by Lensyl Urbano

If you throw a soccer ball up into the air and take a quick series of photographs you can capture the motion of the ball over time. The height of the ball can be measured off the photographs, which can then be used for some interesting physics and mathematics analysis. This assignment focuses on the analysis. It starts with the height of the ball and the time between each photograph already measured (Figure 1 and Table 1).

*Table 1: Height of a thrown soccer ball over a period of approximately 2.5 seconds. This data were taken from a previous experiment on projectile motion.*

Photo | Time (s) | Measured Height (m) |
---|---|---|

P_{0} |
0 | 1.25 |

P_{1} |
0.436396062 | 6.526305882 |

P_{2} |
0.849230104 | 9.825317647 |

P_{3} |
1.262064145 | 11.40310588 |

P_{4} |
1.674898187 | 11.30748235 |

P_{5} |
2.087732229 | 9.657976471 |

P_{6} |
2.50056627 | 6.191623529 |

# Assignment

- Pre-Algebra: Draw a graph showing the height of the ball (y-axis) versus time (x-axis).
- Algebra/Pre-calculus: Determine the equation that describes the height of the ball over time:
*h(t)*. Plot it on a graph. - Calculus: Determine the equation that shows how the velocity of the ball changes over time:
*v(t)*. - Calculus: Determine the equation that shows how the acceleration of the ball changes with time:
*a(t)* - Physics: What does this all mean?

**Citing this post**: **Urbano**, L., 2013. Analyzing the Motion of Soccer Ball using a Camera and Calculus, Retrieved January 20th, 2017, from *Montessori Muddle*: http://MontessoriMuddle.org/ .**Attribution (Curator's Code )**: Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.