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3-044-DeepWell-ModelingScenario

Author(s): Brian Winkel

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

Keywords: gravity projectile motion falling body speed of sound

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Abstract

Resource Image We drop a pebble in a deep well. Given the time elapsed from release of the pebble until we hear the splash determine the depth of the well.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

  • You drop a pebble into a well. Ten seconds later, you hear the sound of the pebble hitting the water. How deep is the well? For what part of the 10 seconds was the pebble falling? How long did it take the sound to travel back up the well? What assumptions did you make in solving the problem?
  • Suppose another well is just that depth at which the time it takes your pebble to hit the water is the same as the time it takes the sound of it hitting the water to return to the top. How deep is this well?
  • Suppose another well is just that depth at which the time it takes your pebble to hit bottom is 15 times greater than the time it takes the sound of it hitting to return to the top. How deep is this well?

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Authors

Author(s): Brian Winkel

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

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