A projectile is any object projected into space (empty or not) by the exertion of a force. Although any object in motion through space (for example a thrown baseball) may be referred to as a projectile, the term more commonly refers to a weapon.
For details of the mathematics surrounding projectile trajectory, see equations of motion.
Read more about Projectile: Motive Force, Delivery Projectiles, Kinetic Projectiles, Wired Projectiles, Typical Projectile Speeds