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...
24 Aug 2019 | | Contributor(s):: Lyle Clifford Smith
After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...
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...
24 Apr 2018 | | Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a first-order 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...
1994-Minton, 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): 436-442.See https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-progression-of-projectiles-examples-from-sports .There is a progression...
2017-Benaka, 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...
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
1999-Long, 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): 127-135.See https://www.tandfonline.com/doi/abs/10.1080/00029890.1999.12005019 .This paper is exactly what it says it is,...