EXPLORING EXCEL SPREADSHEETS TO SIMULATE THE PROJECTILE MOTION IN THE GRAVITATIONAL FIELD

This paper describes an interactive learning tool created with Excel spreadsheets to simulate the projectile motion in the gravitational field taking into account air resistance. The body thrown is considered as point mass and the drag force linear in the speed. The tool allows the analytical and graphical comparison between motion in vacuum and motion in air, in the gravitational field, with the same input data. The trajectory of the body can be viewed in vacuum and in air, separately, for an easier highlight of certain particular aspects, and also comparatively, on the same graph, for a simultaneous observance of differences. For the motion in vacuum, the safety parabola and the ellipse of the points of maximum height have been graphically rendered. For the motion in air, the vertical asymptote of the trajectory has been graphically rendered. For both the motion in vacuum and in air there have been marked on the graphs the maximum height reached by the body and the horizontal distance corresponding to the maximum height. Using the spreadsheet facilities there is provided an approximate method of determining the flight time and the maximum horizontal range for the motion in air. Furthermore, there are comparative presentations of the graphs of velocities and the horizontal and vertical displacements in relation to time. Given the importance of the addressed topic both for ballistics and for various ball sports, the use of the tool in the classroom with the students can be an attractive and motivating factor for the study of Physics. With the rapid graphical feedback to changes in the input data, students can better understand the influence of various parameters on the trajectory and clarify significant concepts such as terminal velocity or the asymptote of a trajectory.