Projectile

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.
In ballistics, mathematical equations of motion are used to analyze projectile trajectories through launch, flight, and impact.

Motive force

s 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 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" : 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 sports

In projectile motion the most important force applied to the projectile mass is the propelling force. In many sports, the propelling forces are provided by muscles that accelerate the projectile, and the stronger the propelling force, the faster and farther the projectile will travel. See pitching, bowling.

As a weapon

Delivery projectiles

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, or poisoning.

Kinetic projectiles

Wired projectiles

Some projectiles stay connected by a cable to the launch equipment after launching it:

for guidance: wire-guided missile
to administer an electric shock, as in the case of a Taser ; two projectiles are shot simultaneously, each with a cable.
to make a connection with the target, either to tow it towards the launcher, as with a whaling harpoon, or to draw the launcher to the target, as a grappling hook does.
Equations of motion

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, = initial velocity 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 covered by the projectile. It is given as.
4. Range : The Range of a projectile is the horizontal distance covered by the projectile. Mathematically,. The Range is maximum when angle = 45°, i.e..