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Modeling Scenario

1-050-BargingAhead-ModelingScenario

Author(s): Timothy Pennings

Davenport University, Grand Rapids MI USA

Keywords: optimization kinetics energy trophic efficiency work river terminal velocity friction current force barge worlk speed

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Abstract

Resource Image As captain of a barge, you need to determine how fast to transport your barge up river against the current in order to minimize the expended energy.

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Differential Equation Type
Technique
Qualitative Analysis
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Technology
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Key Scientific Process Skills
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Pedagogical Approaches
Vision and Change Core Competencies - Ability
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Description

Since expended energy is proportional to the force, and since the force is proportional to the speed, traveling too fast is inefficient. However, if traveling too slow, it will almost take an infinite amount of time to arrive, which is also inefficient.

How fast then should you go?

We find an answer to this question, and to the related question of minimizing cost of travel, where the cost is a linear combination of the energy and the time.

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Authors

Author(s): Timothy Pennings

Davenport University, Grand Rapids MI USA

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