## Resources

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Resource Type (90)

Modeling Scenario(51) Technique Narrative(2) Potential Scenario(31) Article or Presentation(4) Free Online Textbook(2)

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Differential Equation Type (90)

ODE(86) PDE(5) Difference(3) First(22) Second(64) Linear(44) Nonlinear(14) System(21) Constant Coeff(23) Homogeneous(23) Nonhomogeneous(14) Other(1)

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Application Area (90)

Chemistry(3) Economics(2) Engineering(22) Humanities(1) Life Sciences(7) Mathematics(33) Modeling (general)(79) Physics(78) Other(1)

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Calculus 2(23) Calculus 3 (multivariable)(1) Differential Equations(89) Modeling(88)

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Assignment(1) Homework(45) Written assignment: Essay(2) Written assignment: Report(47)

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Pedagogical Approaches (45)

Case Study(3) Computer Model(4) Physical Model(2) Guided inquiry/investigation(41)

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Vision and Change Core Competencies - Ability (49)

Create and develop models(48) Use quantitative reasoning(43) Design simulations(10) Tap into interdisciplinary study(4) Communicate and collaborate with mathematics community(1) Communicate and collaborate with other disciplines(4)

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Principles of How People Learn (50)

Motivates student to learn material(49) Focuses student on the material to be learned(45) Develops supportive community of learners(1) Reveals prior knowledge(4) Requires student to do the bulk of the work(2)

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Bloom's Cognitive Level (50)

Foundational: factual knowledge & comprehension(4) Application & Analysis(49) 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?”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.Modeling Scenario

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

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

##### 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

##### 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,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.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

##### 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

##### 3-095-ShotInWater-ModelingScenario

This project uses Newton's Second Law of Motion in conjunction with a quadratic model for the resistance experienced by a bullet moving through water to analyze a classic action movie scene.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.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.Modeling Scenario

##### 3-054-Relay-ModelingScenario

We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.Article or Presentation