Mastering Projectile Motion: The Science Behind Ballistics & Free Flight

This PowerPoint explores projectile motion, a combination of horizontal uniform motion and vertical acceleration due to gravity. It builds on Galileo’s laws, explaining that in the absence of air resistance:

- Horizontal motion remains at constant velocity.
- Vertical motion follows the same acceleration as free fall (-9.8 m/s²).

Key topics covered:
✔ Parabolic trajectory: Derived from kinematic equations, proving that projectiles follow a symmetrical arc.
✔ Hang time & maximum height: The total time a projectile stays in the air is determined by its initial vertical velocity.
✔ Range of a projectile: The horizontal distance traveled depends on the initial velocity and launch angle.
✔ Optimal launch angle: The maximum range occurs at 45°, based on the equation \\( R_{\\max} = v_0^2 / g \\).
✔ Real-world applications: Military ballistics (e.g., Paris gun of 1918), sports physics, and engineering calculations.