# Projectile Motion

PROJECTILE

A projectile is any object thrown into space upon which the only acting force is gravity. The primary force acting on a projectile is gravity. This doesn’t necessarily mean that other forces do not act on it, just that their effect is minimal compared to gravity. The path followed by a projectile is known as a trajectory.

Examples of projectile:

1. A body dropped from the window of a moving train
2. A bomb released from an airplane.
3. A bullet fired from a rifle
4. A javelin or hammer thrown by an athlete.

## What Is Projectile Motion?

When a particle is thrown obliquely near the earth’s surface, it moves along a curved path under constant acceleration directed towards the centre of the earth (we assume that the particle remains close to the earth’s surface). The path of such a particle is called a projectile, and the motion is called projectile motion.

In a Projectile Motion, there are two simultaneous independent rectilinear motions:

1. Along the x-axis: uniform velocity, responsible for the horizontal (forward) motion of the particle.
2. Along the y-axis: uniform acceleration, responsible for the vertical (downwards) motion of the particle.

Acceleration in the horizontal projectile motion and vertical projectile motion of a particle: When a particle is projected in the air with some speed, the only force acting on it during its time in the air is the acceleration due to gravity (g). This acceleration acts vertically downward. There is no acceleration in the horizontal direction, which means that the velocity of the particle in the horizontal direction remains constant.

PROJECTILE MOTION

If an object is launched at an initial angle of  with the horizontal, the analysis is similar except that the initial velocity has horizontal as well as vertical component. The initial velocity u as shown below:-

NOTE: - Horizontal and vertical components of velocity are independent.

Vertical velocity decreases at a constant rate due to the influence of gravity.

Horizontal velocity will remain constant.

PROJECTILE FIRED PARALLEL TO HORIZONTAL

Projectile Motion on an inclined plane

Let the particle strike the plane at A so that OA is the range of the projectile on inclined plane.

1. u cos (α - β) along the plane
2. u sin (α - β) perpendicular to the plane.

The acceleration due to gravity g can be resolved into two components:

1. g sin β parallel to the plane
2. g cos β perpendicular to the plane.

Projectile Motion on an inclined plane

Time of Flight:

Let t be the time taken by the particle to go from A to B. In this time the displacement of the projectile to the plane is zero.

Hence,

Projectile Motion on an inclined plane

Range:

During time of flight, the horizontal velocity u cos α remains constant.

Hence,     Horizontal distance

Projectile motion has many applications in the real world, including:

• Sports: Projectile motion is used in many sports, such as baseball, basketball, football, golf, and soccer. For example, a baseball pitcher uses projectile motion to throw the ball to the catcher. A basketball player uses projectile motion to shoot the ball into the hoop. A football player uses projectile motion to throw the ball to a teammate. A golfer uses projectile motion to hit the ball into the hole. A soccer player uses projectile motion to kick the ball into the goal.
• Engineering: Projectile motion is used in many engineering applications, such as designing artillery weapons, missiles, and rockets. For example, artillery weapons use projectile motion to fire shells at long distances. Missiles use projectile motion to travel long distances and reach high altitudes. Rockets use projectile motion to launch into space.
• Military science: Projectile motion is used in many military applications, such as designing artillery weapons, missiles, and rockets. For example, artillery weapons use projectile motion to fire shells at long distances. Missiles use projectile motion to travel long distances and reach high altitudes. Rockets use projectile motion to launch into space.
• Other applications: Projectile motion is also used in other applications, such as designing amusement park rides and designing fire sprinklers. For example, amusement park rides use projectile motion to launch riders into the air. Fire sprinklers use projectile motion to spray water over a wide area.