Unconventional free fall measurements of g: involving the Pythagorean Theorem and inverse tangent function

Abstract

The current work presents unconventional but instructionally useful approaches to data analysis and modelling that allow for measurements of the acceleration due to gravity, g, using free-falling motion and the popular Tracker software. The two techniques detailed in this article illustrate the employability of the Pythagorean Theorem and the inverse tangent function in modelling free-falling motion that likewise, expectedly, permit for the determination of g. These two mathematical concepts are brought to relevance by strategically situating the origin of the coordinate system at an appropriate point. The models returned values of the gravitational acceleration that are comparable to that by the traditional technique, the one directly based on the vertical position-time data. Additionally, the unconventional free-fall data analyses presented in this paper suggest extra and insightful activities for the students, exercises on a notably less-automated nonlinear curve fitting on a spreadsheet (MS Excel) at most. Ultimately, by applying familiar mathematical concepts associated with a right triangle to nontraditional contexts like free-fall, this laboratory or lecture activity is perceived to spark greater interest of the students and enhance learning by unifying theory and experimental data.