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    Modeling Scenario
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    1-050-BargingAhead-ModelingScenario
    As captain of a barge, you need to determine how fast to transport your barge up river against the current in order to minimize the expended energy.
    optimizationkineticsenergytrophic efficiencyworkriverterminal velocityfrictioncurrentforcebargeworlkspeed
    Modeling Scenario
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    1-105-AnimalFall-ModelingScenario
    This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.
    animalNetwon's Second Law of Motionfalling bodyterminal velocityair resistanceNewtonair frictionfall
    Modeling Scenario
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    3-063-FallingBuildingIce-ModelingScenario
    We model the fall of a piece of ice which is falling from a high building in New York City.
    resistancefallinggravityiceterminal velocityskyscrapers
    Modeling Scenario
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    3-103-PullBackCars-ModelingScenario
    This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.
    modelingdynamicshands-ontoypull-back carpullback
    Modeling Scenario
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    1-013-SleuthingWithDifferentialEquations-ModelingScenario
    We present several situations in which differential equation models serve to aid in sleuthing and general investigations.
    projectile motionaccelerationNewton's Law of Coolingspeeding
    Modeling Scenario
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    1-068-WaterBottleCooling-ModelingScenario
    Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.
    bNewton's Law of Coolingwater bottleautonomousbottle
    Modeling Scenario
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    1-060-SalesMarketing-ModelingScenario
    We lead students through a sales forecasting model based on marketing principles first espoused by F. M. Bass with definitions, assumptions, equations, and data on sales over 15 year periods against which models may be tested.
    marketingBass modelsalesconsumer productsinnovatorsimitators
    Modeling Scenario
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    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.
    distanceprojectile motionrelaytimebaseballoutfieldhome plateminimization
    Modeling Scenario
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    5-036-HalfCarVibration-ModelingScenario
    Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF) including pitch and bounce of vehicle body on suspension...
    vibrationvehiclehalf-car modelfinite element analysisshock absorberssuspension
    Modeling Scenario
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    6-023-DroneHeadingHome-ModelingScenario
    We describe a comprehensive project in modeling through a two dimensional system of equations and a first order system of differential equations a drone heading home.
    dronesoursuitflight pathchange of variables
    Modeling Scenario
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    1-116-TropicalStormWindspeeds-ModelingScenario
    We model the decay of tropical cyclone winds once a storm makes landfall. We use data from two recent storms from the National Hurricane Center to estimate parameters emanating from a differential equation using a first order exponential decay model.
    hurricanedecaytropical stormcyclones
    Modeling Scenario
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    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.
    projectile motioncatapultuphilllaunch angle
    Modeling Scenario
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    6-008-PursuitModels-Modeling Scenario
    Students are prompted to build systems of nonlinear differential equations to model pursuit-evader activities in which a pursuer attempts to follow, perhaps track down and come close to, an evader without knowledge of the evader's intentions, just...