Projectile motion

Encyclopedia

The motion in which a body is thrown or projected is called

The path followed by a projectile is called its trajectory

, which is directly influenced by gravity.

The initial velocity

The components

and

The horizontal motion and the vertical motion are independent of each other ; that is, neither motion affects the other.

Since there is no acceleration in the horizontal direction, the horizontal component of the velocity remains unchanged throughout the motion.

The vertical motion is the motion of a particle in free fall. Equations for free fall apply. For example,

.

Other useful equations for the vertical y-axis are

,

and

.

Eliminating t between the following two equations,

and ,

we obtain the equation of the path (the trajectory) of the projectile:

Time to reach the maximum height

Time to reach ground

Displacement in X direction

Displacement in Y direction

Range of projectile

Maximum height

in which a and b are constants. This is the equation of a parabola, so the path is parabolic.

The horizontal range R of the projectile is the horizontal distance the projectile has travelled when it returns to its initial height:

Note that R has its maximum value when , which necessarily corresponds to or .

**Projectile motion.**The path followed by a projectile is called its trajectory

Trajectory

A trajectory is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example. It thus includes the meaning of orbit—the path of a planet, an asteroid or a comet as it travels around a central mass...

, which is directly influenced by gravity.

The initial velocity

*v*_{0}can be written asThe components

*v*_{0x}and*v*_{0y}can be found if the angle θ_{0}is known:and

The horizontal motion and the vertical motion are independent of each other ; that is, neither motion affects the other.

Since there is no acceleration in the horizontal direction, the horizontal component of the velocity remains unchanged throughout the motion.

The vertical motion is the motion of a particle in free fall. Equations for free fall apply. For example,

.

Other useful equations for the vertical y-axis are

,

and

.

Eliminating t between the following two equations,

and ,

we obtain the equation of the path (the trajectory) of the projectile:

Time to reach the maximum height

Time to reach ground

Displacement in X direction

Displacement in Y direction

Range of projectile

Maximum height

## Parabolic trajectory

Since , , and are constants, the above equation is of the form,in which a and b are constants. This is the equation of a parabola, so the path is parabolic.

The horizontal range R of the projectile is the horizontal distance the projectile has travelled when it returns to its initial height:

Note that R has its maximum value when , which necessarily corresponds to or .

## See also

- KinematicsKinematicsKinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
- Range of a projectileRange of a projectileright|thumb|250 px|The path of this projectile launched from a height y0 has a range d.In physics, assuming a flat Earth with a uniform gravity field, a projectile launched with specific initial conditions will have a predictable range. As in Trajectory of a projectile, we will use:The following...
- TrajectoryTrajectoryA trajectory is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example. It thus includes the meaning of orbit—the path of a planet, an asteroid or a comet as it travels around a central mass...
- Trajectory of a projectileTrajectory of a projectileIn physics, the ballistic trajectory of a projectile is the path that a thrown or launched projectile will take under the action of gravity, neglecting all other forces, such as friction from air resistance, without propulsion....