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Modeling Scenario

3-015-StyrofoamBallFall-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: football resistance gravity falling body sum of square errors Newton's Second Law of Motion sum of forces styrofoam

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Abstract

Resource Image We are given data on a falling Styrofoam ball and we seek to model this motion.

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Description

We propose two models for y(t) the distance fallen by the Styrofoam ball in meters at time $t$ in seconds in which positive distances and velocities are downward.

  1. The ball meets with resistance due to the air which is proportional to velocity, y'(t). We model this with - a y'(t) where we presume a is positive.
  2.  The ball meets with resistance due to the air which is proportional to velocity squared, y'(t)2. We model this with - a y'(t)2 where we presume a is positive.

In both cases (1) and (2) we seek to determine the parameter a such that the model fits the data best in the sense of minimizing the sum of square errors between the observed data and the model over all data points.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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