Abstract

Citation

Researchers should cite this work as follows:

• Winkel, B. (2022). 3-015-StyrofoamBallFall-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/Q4HP-SC29

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Article Context

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.