proyectile

A projectile is an object that is launched or thrown into motion with an initial velocity, and whose subsequent trajectory is governed by external forces such as gravity and air resistance. It is distinguished from objects that continue to propel themselves or are guided by an onboard propulsion system during flight.

In the idealized case of negligible air resistance, projectile motion is described by simple kinematics. The horizontal position changes as x = v0 cos(θ) t, while the vertical position follows y = v0 sin(θ) t − 1/2 g t^2, where v0 is the launch speed, θ is the launch angle, and g is the acceleration due to gravity. The range for a level launch is R = v0^2 sin(2θ) / g, and the maximum height is H = (v0^2 sin^2(θ)) / (2g). These relations assume a vacuum and no lift.

In the real world, air drag and other forces modify the trajectory. Drag opposite to motion reduces range and speed, while drag that depends on velocity and cross-sectional area makes the path diverge from a perfect parabola. Spin, lift, wind, and atmospheric density can further curve or drift the path, and high-speed projectiles may exhibit complex aerodynamic effects.

Common examples of projectiles include bullets, arrows, stones, and sports balls. Guided or motorized projectiles, such as missiles or artillery rounds with propulsion and guidance, use additional forces and control systems to alter their trajectory. The study of projectile motion and ballistics spans physics, engineering, and military science.