## Resources

#####
Resource Type (15)

Modeling Scenario(10) Technique Narrative(1) Potential Scenario(3) Article or Presentation(1)

#####
Differential Equation Type (15)

ODE(14) First(2) Second(10) Linear(8) Nonlinear(2) System(5) Constant Coeff(5) Homogeneous(2) Nonhomogeneous(3)

#####
Technique (15)

Boundary Value Problems(1) Initial Value Problems(13) Numerical Methods(1) Parameter Estimation(2) Qualitative Behavior(1) Separable(1) Separation of Variables(1)

#####
Qualitative Analysis (15)

Graphical analysis(10) Parameters(6) Other(5)

#####
Application Area (15)

Engineering(5) Life Sciences(1) Mathematics(5) Modeling (general)(13) Physics(12)

#####
Course (15)

Calculus 2(3) Calculus 3 (multivariable)(1) Differential Equations(15) Modeling(15)

#####
Course Level (15)

Introductory(15) Upper Level(15) High School(12)

#####
Lesson Length (15)

Portion of one class period(5) One class period(5) Multiple class periods(1) Other(4)

#####
Technology (15)

Mathematica(9) None(1) Other(6)

#####
Approach (15)

Directed(1) Guided(11) Other(4)

#####
Skills (15)

Data collection(2) Data analysis(5) Programming(1) Other(8)

#####
Key Scientific Process Skills (10)

Reviewing prior research(2) Asking a question(9) Formulating hypotheses(6) Predicting outcomes(4) Gathering data/making observations(2) Analyzing data(2) Interpreting results/data(5) Displaying/modeling results/data(5) Communicating results(4)

#####
Assessment Type (11)

Homework(9) Written assignment: Report(10)

#####
Pedagogical Approaches (7)

Case Study(1) Computer Model(1) Physical Model(1) Guided inquiry/investigation(6)

#####
Vision and Change Core Competencies - Ability (9)

Create and develop models(8) Use quantitative reasoning(8) Design simulations(1) Communicate and collaborate with mathematics community(1) Communicate and collaborate with other disciplines(1)

#####
Principles of How People Learn (10)

Motivates student to learn material(9) Focuses student on the material to be learned(9) Reveals prior knowledge(3) Requires student to do the bulk of the work(1)

#####
Bloom's Cognitive Level (11)

Foundational: factual knowledge & comprehension(2) Application & Analysis(10)

#####
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

##### 3-042-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

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

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

##### 3-035-StadiumDesign-ModelingScenario

For a given baseball playing field outline how high must the outfield fence be at each point in order to make a homerun equally likely in all fair directions?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.Modeling Scenario

##### 3-085-SimplePendulum-ModelingScenario

Thestudent is asked to derive and solve a differential equation that gives the position (angleModeling Scenario

##### 1-128-RocketFlight-ModelingScenario

We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its...Modeling Scenario

##### 3-020-ChordPathTime-ModelingScenario

Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is nonintuitive and challenging to understand.Modeling Scenario

##### 3-034-CarSuspension-ModelingScenario

We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.Potential Scenario

##### 1989-R_Blickhan-Spring Mass Model For Running-Hopping

A simple spring—mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed.Article or Presentation

##### 2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne

This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.Modeling Scenario

##### 5-090-SolidParticleErosion-ModelingScenario

By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface.Technique Narrative