A computational and pedagogical framework for projectile motion using Python visualizations

Projectile motion is one of the most fundamental problems in introductory physics, offering a clear context to connect algebraic reasoning with conceptual understanding. This work presents a computational and pedagogical framework that combines the analytical formulation of projectile motion with interactive visualizations developed in Python. Using reproducible simulations, the dependence of the maximum height and horizontal range on the launch parameters $(v_0,θ)$ is examined through trajectory plots, parameter-space maps, and iso-curves. These visual representations reveal non-trivial combinations of initial conditions that yield equivalent outcomes, reinforcing physical intuition and providing an accessible open-source tool for teaching and learning classical mechanics.