projektile

Projektile is the German term for projectile, referring to any object launched into motion that continues along a trajectory primarily under the influence of external forces after propulsion ends. In everyday use, projectiles include bullets, arrows, shells, and sporting objects launched by a catapult or hand.

In the idealized case of negligible air resistance, projectile motion can be analyzed by splitting motion into horizontal and vertical components. The horizontal velocity remains constant; vertical velocity changes due to gravity. The trajectory for a given speed v0 and launch angle theta is a parabola. Time of flight T = 2 v0 sin theta / g; horizontal range R = v0^2 sin 2 theta / g; maximum height H = v0^2 sin^2 theta / (2 g).

In real environments air drag and, to a lesser extent, lift alter the path; drag depends on velocity, cross-sectional area, drag coefficient, and air density. Because drag is velocity dependent, the equations of motion are nonlinear and are usually solved numerically or with approximations. Drag and wind can significantly affect range, height, and flight time, especially for high-speed or long-range projectiles.

The term projectile also distinguishes unpowered objects from missiles or rockets, which are self-propelled after launch. Practically, projectiles are analyzed in fields such as ballistics, sports science, and engineering, where measurements and models estimate trajectories, impact points, and energy considerations.

Historically, the study of projectile motion contributed to developments in kinematics and Newtonian mechanics, with early experiments by Galileo and subsequent formalization within classical physics.