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Views
Date
Relevance
Potential Scenario
139
views
44
downloads
0
comments
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?”
optimization
projectile motion
launch angle
Modeling Scenario
280
views
167
downloads
0
comments
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.
projectile motion
inclined ramp
coefficient of restitution
optimal angle
bounce
Modeling Scenario
244
views
182
downloads
0
comments
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 motion
catapult
uphill
launch angle
Modeling Scenario
1093
views
179
downloads
0
comments
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.
trajectory
launching radiant
projectile motion
projectile
no resistance
angle of launch
Modeling Scenario
268
views
115
downloads
0
comments
3-085-SimplePendulum-ModelingScenario
Thestudent is asked to derive and solve a differential equation that gives the position (angle
Newton's Second Law of Motion
pendulum
kinetic energy
potential energy
Conservation of Energyt
initial conditions
small angle approximation
Taylor polynomial
percent error
Modeling Scenario
474
views
243
downloads
0
comments
6-005-InsectColonySurvivalOpt-ModelingScenario
We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.
optimization
Optimal Control Theory
insect colony
optimal control
natural resources
Pointryagin's Maximum Principle
control variable
Modeling Scenario
184
views
63
downloads
0
comments
3-052-OptimalProjectileFiring-ModelingScenario
We offer the opportunity to model a projectile's trajectory in several cases, all without resistance.
projectile motion
projectile
launch angle
maximum range
Modeling Scenario
295
views
289
downloads
0
comments
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?
projectile motion
baseball
parametric equation
stadium
home run
no reistant
fairness
no resistance
Modeling Scenario
214
views
114
downloads
0
comments
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.
Unit Circle
path
falling
gravity
chord
Netwon's Second Law of Motion
Modeling Scenario
348
views
244
downloads
0
comments
5-007-ChemOpt-ModelingScenario
Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.
optimization
p
Yield and sustainability
nonprofit management
Law of Mass Action
kinetic
reaction
Modeling Scenario
746
views
741
downloads
0
comments
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.
design
spring-mass-dashpot
spring constant
underdamping
car suspension
suspension tolerance
static equilibrium
Modeling Scenario
402
views
500
downloads
0
comments
1-047a-CondensationOptimization-ModelingScenario
We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.
simulation
data
optimization
energy
condensation
best fit
cost
sum of scquare errors
Modeling Scenario
257
views
262
downloads
0
comments
1-079-HomeHeating-ModelingScenario
This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?
Optimal Control Theory
temperature
heat
furnace
Newton's Law of Cooling
home heating
specific heat
Modeling Scenario
300
views
133
downloads
0
comments
1-118-SolowEconomicGrowth-ModelingScenario
Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics.
optimization
economics
steady state
growth
Solow-Swan model
capital
production
labor
Golden Rule of Economic Growth
Potential Scenario
194
views
60
downloads
0
comments
2013-Gonzalez_Parra-Arenas-Mathematical Model for Social Security Systems with Dynamical Systems
In this paper it is proposed a mathematical approach based on dynamic systems to study the effect of the increase in the Social Security normal retirement age on the worker and on the dynamics of retiree populations.
dynamical systems
retirement model
Social Security
Modeling Scenario
666
views
712
downloads
0
comments
3-043-BallisticModeling-SpongeDart-ModelingScenario
The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.
projectile motion
air resistance
ballistics
dimensional analysis
Newtonian mechanics
sponge dart
Nerf gun
Nerf dart
Buckingham's Theorem
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