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

#### by Lensyl Urbano

Animation showing the motion of the ballistic motion of a soccer ball.

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).

Figure 1. Height of a thrown ball, measured off a series of photographs. The photographs have been overlaid to create this image of multiple balls.

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)
P0 0 1.25
P1 0.436396062 6.526305882
P2 0.849230104 9.825317647
P3 1.262064145 11.40310588
P4 1.674898187 11.30748235
P5 2.087732229 9.657976471
P6 2.50056627 6.191623529

# Assignment

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

Citing this post: Urbano, L., 2013. Analyzing the Motion of Soccer Ball using a Camera and Calculus, Retrieved March 27th, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.