%0 Journal Article
%T What Projective Angle Makes the Arc-Length of the Trajectory in a Resistive Media Maximum? A Reverse Engineering Approach
%A Haiduke Sarafian
%J American Journal of Computational Mathematics
%P 71-82
%@ 2161-1211
%D 2021
%I Scientific Research Publishing
%R 10.4236/ajcm.2021.112007
%X We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different velocity-dependent resistive media models are considered¡ªlinear and quadratic. With an objective to utilizing a Computer Algebra System (CAS), specifically <em>Mathematica</em> [1] numerically we solve the corresponding equations of motions. For a set of compatible parameters characterizing viscose forces graphically we display comparing the trajectories explicitly showing the impact of the models. Utilizing the model-dependent trajectory equations numerically we evaluate their associated arc-lengths. What distinguishes our approach vs. the existing body of work is the notion of the ¡°reverse engineering¡±. Meaning, utilizing our numeric data we establish their corresponding analytic counter parts. Ultimately, utilizing both outputs numerically and analytically we determine the matching initial projectile angles maximizing their respective arc-lengths.
%K Velocity Dependent Resistive Media
%K Trajectory Arc-Length
%K Maximizing Angle
%K Computer Algebra System
%K &lt
%K i&gt
%K Mathematica&lt
%K /i&gt
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=109013