
4039SFallingDarts
21 Jan 2022   Contributor(s):: Jacob Paul Duncan
Most projectile motion and free fall models are based on the assumption that gravity is the only force acting on the object. Here we develop, solve, and analyze a second order nonhomogeneous differential equation model for free fall which incorporates air resistance. Students will solve the model...

1083SFallingMeteorites
24 Aug 2019   Contributor(s):: Lyle Clifford Smith
After introducing the solution to the ordinary differential equation which models a falling object with drag (firstorder, nonlinear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

3011SEulerBallThrowing
19 Aug 2019   Contributor(s):: Chris McCarthy
If a tennis ball is thrown through the air it will eventually hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the thrower taking into account air...

6070SBeerBubbles
24 Apr 2018   Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...

1994Minton, Roland  A Progression of Projectiles  Examples from Sports.
12 Sep 2017   Contributor(s):: Brian Winkel
Minton, Roland. 1994. A Progression of Projectiles  Examples from Sports. The College Mathematics Teacher. 28(5): 436442.See https://www.maa.org/programs/facultyanddepartments/classroomcapsulesandnotes/aprogressionofprojectilesexamplesfromsports .There is a progression...

2017Benaka, Jan and Sona Ceretkova  Free fall in a vacuum and in the air – calculating limits using a real example and demonstrating the limiting process to high school students using Excel.
05 Sep 2017   Contributor(s):: Brian Winkel
Benaka, Jan and Sona Ceretkova. 2017. Free fall in a vacuum and in the air – calculating limits using a real example and demonstrating the limiting process to high school students using Excel. Spreadsheets in Education. 9(1): Article 3.Abstract: The paper gives the result of an...

1115SModelingWithFirstOrderODEs
04 Sep 2017   Contributor(s):: Michael Grayling
Several models using first order differential equations are offered with some questions on formulating a differential equations model

1999Long, Lyle N. and Harold Weiss  The Velocity Dependence of Aerodynamic Drag: A Primer for Mathematicians
20 Jun 2015   Contributor(s):: Lyle N. Long, Harold Weiss
Long, Lyle N. and Harold Weiss. 1999. The Velocity Dependence of Aerodynamic Drag: A Primer for Mathematicians. The American Mathematical Monthly. 106(2): 127135.See https://www.tandfonline.com/doi/abs/10.1080/00029890.1999.12005019 .This paper is exactly what it says it is,...