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A projectile is an object that is propelled by the application of an external force and then moves freely under the influence of gravity and air resistance.   Although any objects in motion through space are projectiles, they are commonly found in warfare and sports (for example, a thrown baseball, kicked football, fired bullet, shot arrow, stone released from catapult).  
In ballistics mathematical equations of motion are used to analyze projectile trajectories through launch, flight, and impact.
Blowguns and pneumatic rifles use compressed gases, while most other guns and cannons utilize expanding gases liberated by sudden chemical reactions by propellants like smokeless powder. Light-gas guns use a combination of these mechanisms.
Railguns utilize electromagnetic fields to provide a constant acceleration along the entire length of the device, greatly increasing the muzzle velocity.
Some projectiles provide propulsion during flight by means of a rocket engine or jet engine. In military terminology, a rocket is unguided, while a missile is guided. Note the two meanings of "rocket" (weapon and engine): an ICBM is a guided missile with a rocket engine.
An explosion, whether or not by a weapon, causes the debris to act as multiple high velocity projectiles. An explosive weapon or device may also be designed to produce many high velocity projectiles by the break-up of its casing; these are correctly termed fragments .
In projectile motion the most important force applied to the ‘projectile’ is the propelling force, in this case the propelling forces are the muscles that act upon the ball to make it move, and the stronger the force applied, the more propelling force, which means the projectile (the ball) will travel farther. See pitching, bowling.
Many projectiles, e.g. shells, may carry an explosive charge or another chemical or biological substance. Aside from explosive payload, a projectile can be designed to cause special damage, e.g. fire (see also early thermal weapons), or poisoning (see also arrow poison).
A kinetic energy weapon (also known as kinetic weapon, kinetic energy warhead, kinetic warhead, kinetic projectile, kinetic kill vehicle) is a weapon based solely on a projectile's kinetic energy instead of an explosive or any other kind of payload.
The term Hit-to-kill, or kinetic kill, is also used in the military aerospace field to describe kinetic energy weapons. It has been used primarily in the anti-ballistic missiles (ABM) and anti-satellite weapons (ASAT) area, but some modern anti-aircraft missiles are also hit-to-kill. Hit-to-kill systems are part of the wider class of kinetic projectiles, a class that has widespread use in the anti-tank field.Typical kinetic energy weapons are blunt projectiles such as rocks and round shots, pointed ones such as arrows, and somewhat pointed ones such as bullets. Among projectiles that do not contain explosives are those launched from railguns, coilguns, and mass drivers, as well as kinetic energy penetrators. All of these weapons work by attaining a high muzzle velocity, or initial velocity, generally up to hypervelocity, and collide with their targets, converting the kinetic energy associated with the relative velocity between the two objects into destructive shock waves and heat. Other types of kinetic weapons are accelerated over time by a rocket engine, or by gravity. In either case, it is this kinetic energy that destroys its target.
Some projectiles stay connected by a cable to the launch equipment after launching it:
This section's factual accuracy is disputed .(December 2018)
|Projectile||Speed||Specific kinetic energy (J/kg)|
|Object falling 1 m (in vacuum, at Earth's surface)||4.43||15.948||14.5||9.9||9.8|
|Object falling 10 m (in vacuum, at Earth's surface)||14||50.4||46||31||98|
|Thrown club (expert thrower)||40||144||130||90||800|
|Object falling 100 m (in vacuum, at Earth's surface)||45||162||150||100||980|
|Refined (flexible) atlatl dart (expert thrower)||45||162||150||100||1,000|
|Ice hockey puck (slapshot, professional player)||50||180||165||110||1,300|
|80-lb-draw pistol crossbow bolt||58||208.8||190||130||1,700|
|War arrow shot from a 150 lbs medieval warbow||63||228.2||208||141||2,000|
|Blunt Impact Projectile shot from a 40mm grenade launcher||87||313.2||285||194.6||3,785|
|Paintball fired from marker||91||327.6||300||204||4,100|
|175-lb-draw crossbow bolt||97||349.2||320||217||4,700|
|6 mm Airsoft pellet||100||360||328||224||5,000|
|Air Rifle BB 4.5 mm||150||540||492||336||11,000|
|Air gun pellet .177" (magnum-power air rifle)||305||878.4||1,000||545||29,800|
|9×19mm (bullet of a pistol)||340||1224||1,116||761||58,000|
|12.7×99 mm (bullet of a heavy machine gun)||800||2,880||2,625||1,790||320,000|
|German Tiger I 88 mm (tank shell- Pzgr. 39 APCBCHE)||810||2,899||2,657||1,812||328,050|
|5.56×45mm (standard round used in many modern rifles)||920||3,312||3,018||2,058||470,000|
|20×102mm (standard US cannon round used in fighter cannons)||1,039||3,741||3,410||2,325||540,000|
|25×140mm (APFSDS, tank penetrator)||1,700||6,120||5,577||3,803||1,400,000|
|2 kg tungsten Slug (from Experimental Railgun)||3,000||10,800||9,843||6,711||4,500,000|
|MRBM reentry vehicle||Up to 4,000||Up to 14,000||Up to 13,000||Up to 9,000||Up to 8,000,000|
|projectile of a light-gas gun||Up to 7,000||Up to 25,000||Up to 23,000||Up to 16,000||Up to 24,000,000|
|Satellite in low Earth orbit||8,000||29,000||26,000||19,000||32,000,000|
|Exoatmospheric Kill Vehicle||~10,000||~36,000||~33,000||~22,000||~50,000,000|
|Projectile (e.g., space debris) and target both in low Earth orbit||0–16,000||~58,000||~53,000||~36,000||~130,000,000|
|7 T eV particle in LHC ||299,792,455 [note 1]||1,079,252,839||983571079||670,616,536||~6.7 × 1020 [note 2]|
An object projected at an angle to the horizontal has both the vertical and horizontal components of velocity. The vertical component of the velocity on the y-axis is given as while the horizontal component of the velocity is . There are various calculations for projectiles at a specific angle :
1. Time to reach maximum height. It is symbolized as (), which is the time taken for the projectile to reach the maximum height from the plane of projection. Mathematically, it is given as where = acceleration due to gravity (app 9.81 m/s²), = initial velocity (m/s) and = angle made by the projectile with the horizontal axis.
2. Time of flight (): this is the total time taken for the projectile to fall back to the same plane from which it was projected. Mathematically it is given as .
3. Maximum Height (): this is the maximum height attained by the projectile OR the maximum displacement on the vertical axis (y-axis) covered by the projectile. It is given as .
4. Range (): The Range of a projectile is the horizontal distance covered (on the x-axis) by the projectile. Mathematically, . The Range is maximum when angle = 45°, i.e. .
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called free nutation or Euler nutation. A pure nutation is a movement of a rotational axis such that the first Euler angle is constant. Therefore it can be seen that the circular red arrow in the diagram indicates the combined effects of precession and nutation, while nutation in the absence of precession would only change the tilt from vertical. However, in spacecraft dynamics, precession is sometimes referred to as nutation.
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
A rocket is a vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely from propellant carried within the vehicle; therefore a rocket can fly in the vacuum of space. Rockets work more efficiently in a vacuum and incur a loss of thrust due to the opposing pressure of the atmosphere.
The kinetic theory of gases is a simple, historically significant classical model of the thermodynamic behavior of gases, with which many principal concepts of thermodynamics were established. The model describes a gas as a large number of identical submicroscopic particles, all of which are in constant, rapid, random motion. Their size is assumed to be much smaller than the average distance between the particles. The particles undergo random elastic collisions between themselves and with the enclosing walls of the container. The basic version of the model describes the ideal gas, and considers no other interactions between the particles.
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control.
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.
Recoil is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, as according to Newton's third law the force required to accelerate something will evoke an equal but opposite reactional force, which means the forward momentum gained by the projectile and exhaust gases (ejectae) will be mathematically balanced out by an equal and opposite momentum exerted back upon the gun. In hand-held small arms, the recoil momentum will be eventually transferred to the ground, but will do so through the body of the shooter hence resulting in a noticeable impulse commonly referred to as a "kick".
A railgun is a linear motor device, typically designed as a weapon, that uses electromagnetic force to launch high velocity projectiles. The projectile normally does not contain explosives, instead relying on the projectile's high speed, mass, and kinetic energy to inflict damage. The railgun uses a pair of parallel conductors (rails), along which a sliding armature is accelerated by the electromagnetic effects of a current that flows down one rail, into the armature and then back along the other rail. It is based on principles similar to those of the homopolar motor.
An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and without additional help will fall over. It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced. The inverted pendulum is a classic problem in dynamics and control theory and is used as a benchmark for testing control strategies. It is often implemented with the pivot point mounted on a cart that can move horizontally under control of an electronic servo system as shown in the photo; this is called a cart and pole apparatus. Most applications limit the pendulum to 1 degree of freedom by affixing the pole to an axis of rotation. Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright; this can be done either by applying a torque at the pivot point, by moving the pivot point horizontally as part of a feedback system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot point vertically. A simple demonstration of moving the pivot point in a feedback system is achieved by balancing an upturned broomstick on the end of one's finger.
A sub-orbital spaceflight is a spaceflight in which the spacecraft reaches outer space, but its trajectory intersects the atmosphere or surface of the gravitating body from which it was launched, so that it will not complete one orbital revolution or reach escape velocity.
Projectile motion is a form of motion experienced by an object or particle that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particular case of projectile motion of Earth, most calculations assume the effects of air resistance are passive and negligible. The curved path of objects in projectile motion was shown by Galileo to be a parabola, but may also be a straight line in the special case when it is thrown directly upwards. The study of such motions is called ballistics, and such a trajectory is a ballistic trajectory. 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 the Earth’s center of mass. Because of the object's inertia, no external force is needed to maintain the horizontal velocity component of the object's motion. Taking other forces into account, such as aerodynamic drag or internal propulsion, requires additional analysis. A ballistic missile is a missile only guided during the relatively brief initial powered phase of flight, and whose remaining course is governed by the laws of classical mechanics.
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance, has an orbit that is a conic section with the central body located at one of the two foci, or the focus.
A ranged weapon is any weapon that can engage targets beyond hand-to-hand distance, i.e. at distances greater than the physical reach of the user holding the weapon itself. The act of using such a weapon is also known as shooting. It is sometimes also called projectile weapon or missile weapon because it typically works by launching solid projectiles ("missiles"), though technically a fluid-projector and a directed-energy weapon are also ranged weapons. In contrast, a weapon intended to be used in hand-to-hand combat is called a melee weapon.
Spacecraft flight dynamics is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and aerodynamic lift and drag.
A banked turn is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. The bank angle is the angle at which the vehicle is inclined about its longitudinal axis with respect to the horizontal.
A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging it back and forth. The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations.
In physics, a projectile launched with specific initial conditions will have a range. It may be more predictable assuming a flat Earth with a uniform gravity field, and no air resistance.
In celestial mechanics, a Kepler orbit is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. A Kepler orbit can also form a straight line. It considers only the point-like gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag, solar radiation pressure, a non-spherical central body, and so on. It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem. As a theory in classical mechanics, it also does not take into account the effects of general relativity. Keplerian orbits can be parametrized into six orbital elements in various ways..
A kinetic energy weapon is a weapon based solely on a projectile's kinetic energy instead of an explosive or any other kind of payload.
The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body. Several aspects of a bouncing ball's behaviour serve as an introduction to mechanics in high school or undergraduate level physics courses. However, the exact modelling of the behaviour is complex and of interest in sports engineering.