Projectile Motion proof

The video tutorial explains the derivation of projectile motion formulas by considering a ball thrown into the air. It covers the initial conditions, vertical and horizontal motion analysis using calculus, and assumptions like no aerodynamic drag and constant gravity. The tutorial concludes with a note on the parabolic path of the projectile.

What are the equations that describe the vertical position of a projectile at any time T?

What assumptions are made regarding forces acting on a projectile during its flight?

How can the path of a projectile be proven to be a parabola?