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Modeling Scenario

6-012-RiverCrossing-ModelingScenario

Author(s): Brian Winkel

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

Keywords: dragon Newton's Second Law of Motion river crossin river current velocity profile thrust Free Body Diagram

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Abstract

Resource Image Students develop a model of a river crossing in a boat with thrust using Newton's Second Law of Motion from a Free Body Diagram they construct. The model is thence a system of one second order linear and a second order nonlinear differential equations.

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Description

Students must construct a river current model from some general notions and three data points on the flow magnitudes to incorporate into the model.

With a given set of parameters we see where the boat lands on the other side of the river and then we seek changes in parameters to be sure the boat arrives at a specified landing point on the other side of the river?

We offer a number of ``What if'' issues once the model has been developed beyond the obvious question of, ``Where does the boat land downstream on the East bank knowing its West bank starting point?''

For example, given different river current parameters in what direction might the boat head in order to arrive at the same landing point under each set of conditions?

If we make the flow of the river asymmetric about its central line or axis how does this change the landing spot on the East bank, if all other things are left the same?

If we fix the heading of the boat then for various river current parameters what thrust is necessary to arrive at the same landing point under each set of conditions?

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Authors

Author(s): Brian Winkel

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

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