Editing Projectile motion (section)

{{Short description|Motion of launched objects due to gravity}}
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[[File:ParabolicWaterTrajectory.jpg|thumb|250px|[[Parabolic trajectory|Parabolic trajectories]] of water jets]]
[[File:Ferde hajitas2.svg|thumb|250px|Components of initial velocity of parabolic throwing]]
[[File:Ballistic trajectories.svg|thumb|250px|Ballistic trajectories are parabolic if gravity is homogeneous and elliptic if it is radial.]]

In physics, projectile motion describes the motion of an object that is launched into the air and moves under the influence of gravity alone, with air resistance neglected. In this idealized model, the object follows a parabolic path determined by its initial velocity and the constant acceleration due to gravity. The motion can be decomposed into horizontal and vertical components: the horizontal motion occurs at a constant velocity, while the vertical motion experiences uniform acceleration.

This framework, which lies at the heart of classical mechanics, is fundamental to a wide range of applications—from engineering and ballistics to sports science and natural phenomena.

[[Galileo Galilei]] showed that the trajectory of a given projectile is [[parabolic trajectory|parabolic]], but the path may also be [[line (geometry)|straight]] in the special case when the object is thrown directly upward or downward. The study of such motions is called [[ballistics]], and such a trajectory is described as [[external ballistics|ballistic]]. The only force of mathematical significance that is actively exerted on the object is gravity, which acts downward, thus imparting to the object a downward [[acceleration]] towards Earth's [[center of mass]]. Due to the object's [[inertia]], no external force is needed to maintain the horizontal velocity [[vector component|component]] of the object's motion.

Taking other forces into account, such as [[drag (physics)|aerodynamic drag]] or internal propulsion (such as in a [[rocket]]), requires additional analysis. A [[ballistic missile]] is a [[missile]] only [[missile guidance|guided]] during the relatively brief initial [[powered flight|powered]] phase of flight, and whose remaining course is governed by the laws of [[classical mechanics]].

Ballistics ({{etymology|grc|''{{Wikt-lang|grc|βάλλειν}}'' {{grc-transl|βάλλειν}}|to throw}}) is the science of [[dynamics (physics)|dynamics]] that deals with the flight, behavior and effects of projectiles, especially [[bullet]]s, [[unguided bomb]]s, [[rocket]]s, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.

[[File:Mplwp ballistic trajectories velocities.svg|right|thumb|320px|Trajectories of a projectile with air drag and varying initial velocities]]

The elementary equations of ballistics neglect nearly every factor except for initial velocity, the launch angle and a gravitational acceleration assumed constant. Practical solutions of a ballistics problem often require considerations of air resistance, cross winds, target motion, acceleration due to gravity varying with height, and in such problems as [[Berlin rocket launching site|launching a rocket]] from one point on the Earth to another, the horizon's distance ''vs'' curvature R of the Earth (its local speed of rotation <math display="inline">v(lat)=\omega R(lat)</math>). Detailed mathematical solutions of practical problems typically do not have [[closed-form expression|closed-form]] solutions, and therefore require [[numerical methods]] to address.