TITLE:
Mass Dependent Computational Analysis of Projectile Motion under Quadratic Air Drag Using the Runge-Kutta Method
AUTHORS:
Annasi Ayubu Said, Haroub Pollycap Mbewe, Melckzedeck Michael Mgimba, Hassani Saidi Namanolo, Shadya Muhammed Rashid, Sumaiya Issa Ussi
KEYWORDS:
Projectile Motion, Air Resistance, Quadratic Drag, Nonlinear Dynamics, Numerical Simulation, Mass Dependence
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.15 No.12,
December
22,
2025
ABSTRACT: This study investigates projectile motion under quadratic air drag, focusing on mass-dependent dynamics using the Runge-Kutta (RK4) method implemented in FreeMat. Quadratic drag, predominant in high Reynolds number flows, significantly alters trajectories and challenges analytical modeling. We examine projectile trajectories for varying masses: 0.046 kg (golf ball), 0.145 kg (baseball), and 0.189 kg (softball) across initial velocities ranging from 10 m/s to 50 m/s. Simulations show that increasing mass yields greater resistance to deceleration, resulting in longer flight ranges and higher terminal velocities. Distinct asymmetries are observed in vertical velocity profiles during ascent and descent, validating theoretical expectations. The study quantifies the influence of mass on terminal velocity, range, and peak height, providing insights applicable to ballistic modeling, sports physics, and atmospheric transport phenomena. The RK4 method demonstrates accuracy and stability in solving nonlinear differential equations governing such dynamics. These findings emphasize the significance of quadratic drag modeling in realistic projectile simulations and provide a validated numerical framework for applications in ballistics, sports physics, and atmospheric dynamics.