Abstract

Shoot a projectile straight up in the air. Determine maximum height the projectile will go. Consider time T(a) (0 < a < 1) it takes between when the projectile passes distance a.H going up and then coming down. Develop T(a) as a function of a.

Citation

Researchers should cite this work as follows:

• Winkel, B. (2022). 3-041-UpDown-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/8XY8-C736

  BibTex | EndNote

Article Context

Resource Type

• Modeling Scenario

Differential Equation Type

• ODE
• Second
• Linear
• Constant Coeff
• Nonhomogeneous

Technique

• Initial Value Problems

Qualitative Analysis

• Graphical analysis
• Other

Application Area

• Modeling (general)
• Physics

Course

• Differential Equations
• Modeling

Course Level

• Introductory
• Upper Level
• High School

Lesson Length

• Portion of one class period

Technology

• Mathematica

Approach

• Guided

Skills

• Data collection
• Data analysis

Key Scientific Process Skills

• Asking a question
• Formulating hypotheses
• Designing/conducting experiments
• Predicting outcomes
• Gathering data/making observations
• Analyzing data
• Interpreting results/data
• Displaying/modeling results/data
• Communicating results

Assessment Type

• Homework
• Written assignment: Report

Pedagogical Approaches

• Guided inquiry/investigation

Vision and Change Core Competencies - Ability

• Create and develop models
• Use quantitative reasoning

Principles of How People Learn

• Motivates student to learn material
• Focuses student on the material to be learned

Bloom's Cognitive Level

• Application & Analysis

Description

See if there are any relationships involving these two times at which the projectile passes through the same distance, going up and coming down.

Article Files

• 3-041-S-UpDown-StudentSersion.pdf(PDF | 390 KB)
• 3-041-S-UpDown-StudentSersion.tex(TEX | 9 KB)
• 3-041-T-Mma-UpDown-TeacherVersion.nb (Instructors only)(NB | 69 KB)
• 3-041-T-Mma-UpDown-TeacherVersion.pdf (Instructors only)(PDF | 123 KB)
• 3-041-T-UpDown-TeacherVersion.pdf (Instructors only)(PDF | 412 KB)
• 3-041-T-UpDown-TeacherVersion.tex (Instructors only)(TEX | 9 KB)
• SIMIODE.cls(CLS | 5 KB)
• SimiodeLogo.jpg(JPG | 271 KB)
• VerticalPic.jpg(JPG | 33 KB)
• License terms

Authors

Author(s): Brian Winkel

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

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