Kinematics in Two Dimensions and Projectile Motion

Prove the principle of independence for perpendicular components of motion and apply it to general 2D trajectories.

Derive the parametric equations of motion (x(t), y(t)) for a projectile under constant gravity.

Derive the trajectory equation, y(x), for projectile motion and prove its parabolic nature.

Derive, with rigorous proofs, the formulas for maximum height, time of flight, and horizontal range of a projectile.

Solve projectile motion problems on an inclined plane by decomposing motion in an optimally chosen coordinate system.