## Resources

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Resource Type (25)

Modeling Scenario(14) Potential Scenario(9) Article or Presentation(2)

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Differential Equation Type (25)

ODE(23) First(6) Second(21) Linear(15) Nonlinear(4) System(7) Constant Coeff(8) Homogeneous(7) Nonhomogeneous(6) Other(1)

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Technique (25)

Boundary Value Problems(1) Initial Value Problems(22) Numerical Methods(4) Parameter Estimation(8) Qualitative Behavior(3) Separable(1) Separation of Variables(2) Other(3)

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Qualitative Analysis (25)

Equilibrium(1) Stability(1) Phase Plane(1) Graphical analysis(12) Parameters(13) Other(8)

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Application Area (25)

Engineering(5) Life Sciences(2) Mathematics(9) Modeling (general)(22) Physics(25) Other(1)

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Course (25)

Calculus 2(9) Differential Equations(24) Modeling(23)

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Course Level (25)

Introductory(25) Upper Level(22) Graduate(1) High School(18)

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Lesson Length (25)

Portion of one class period(9) One class period(4) Multiple class periods(1) Other(11)

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Technology (25)

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Approach (25)

Directed(1) Guided(12) Open-ended(1) Develop model(2) Other(10)

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Skills (25)

Data collection(3) Data analysis(11) Statistics(1) Other(14)

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Key Scientific Process Skills (13)

Asking a question(12) Formulating hypotheses(11) Designing/conducting experiments(3) Predicting outcomes(6) Gathering data/making observations(2) Analyzing data(3) Interpreting results/data(5) Displaying/modeling results/data(5) Communicating results(5)

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Assessment Type (14)

Homework(11) Written assignment: Essay(1) Written assignment: Report(12)

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Pedagogical Approaches (10)

Case Study(1) Computer Model(1) Physical Model(1) Guided inquiry/investigation(9)

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Vision and Change Core Competencies - Ability (12)

Create and develop models(12) Use quantitative reasoning(11) Design simulations(3) Communicate and collaborate with other disciplines(1)

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Principles of How People Learn (13)

Motivates student to learn material(12) Focuses student on the material to be learned(11) Reveals prior knowledge(2) Requires student to do the bulk of the work(2)

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Bloom's Cognitive Level (14)

Foundational: factual knowledge & comprehension(2) Application & Analysis(14) Synthesis/Evaluation/Creation(1)

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Includes clear efforts on Issues (0)

###### Applied Filters

Potential Scenario

##### 2002-Chai-Optimal initial angle to fire a projectile

Assume a projectile is fired without air resistance and lands at a height y above its initial vertical position. What is the optimal initial angle of firing to maximize the horizontal distance traveled by the projectile?”Modeling Scenario

##### 3-052-OptimalProjectileFiring-ModelingScenario

We offer the opportunity to model a projectile's trajectory in several cases, all without resistance.Modeling Scenario

##### 3-042-CatapultLaunch-ModelingScenario

We maximize the range of a projectile by backing up an incline in the opposite direction of the range to give some initial lift. Find the position on the hill from which to launch the projectile to give the best lift.Modeling Scenario

##### 3-051-ProjectileMotions-ModelingScenario

We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.Modeling Scenario

##### 3-041-UpDown-ModelingScenario

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.Potential Scenario

##### 1994-Roland_Minton-A Progression of Projectiles-Examples from Sports

There is a progression of complexity and issues in projectile motion modeling from no resistance, to resistance proportional to velocity, then to velocity squared,Potential Scenario

##### 2017-Ole_Witt-Hansen-Examples Of Differential Equations In Physics

This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena.Potential Scenario

##### 1988- N_Koblitz-Problems that Teach the Obvious but Difficult

Four problems are presented and two of them involve differential equations. These involve projectile motion in one and two dimensions.Modeling Scenario

##### 4-036-AltitudeDependentGravity-ModelingScenario

When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.Modeling Scenario

##### 3-033-S-TimeUpTimeDown-ModelingScenario

We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.Potential Scenario

##### 2006-G_Ashline-J_Ellis-Monaghan-How high-fast-long-Modeling water rocket flight with calculus

We describe an easy and fun project using water rockets to demonstrate applications of single variable calculus concepts.Potential Scenario

##### 2017-Jun_Liu-Hammer Throwing parameters optimization model research based on flight dynamical differential equation

With progress of times, sports techniques are also rapidly developing, in order to let Chinese hammer throwers more quickly improve themselves levels.Modeling Scenario

##### 3-045-RampBounce-ModelingScenario

Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile motion model of the ball bouncing off the ramp.Article or Presentation

##### 1999-F_Brauer-What_Goes_Up_Must_Come_Down

It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum height than it takes to rise to this maximum height for frictional forces that are nonlinear functions of velocity.Modeling Scenario