Ballistics without friction

This lecture introduces the laws of dynamics for a point particle, focusing on the gravitational field. The instructor models the force, chooses a coordinate system, and expresses velocity and acceleration. By applying Newton's law of dynamics, differential equations are derived and integrated. The lecture covers the force proportional to mass, the symbolic equation representing a common difficulty in physics, and the analysis of a physical system through projections. The instructor then integrates the equations of motion, determines initial conditions, and derives the trajectory equation. Simplifying the notation, the instructor defines a new coordinate system to eliminate constants and obtain the trajectory equation in the x-z plane, resulting in a parabolic function.