# What is Projectile Motion? – Types, Derivation, Formulae 2024

Before we delve into the topic, let us first find out what a Projectile is. It is an object that has been thrown into space, on which gravity acts as an opposing force. Moreover, you should also remember that there are other forces acting on the projectile, but they are very minimal. The acting of different forces as well as the magnitude of gravitational forces depends on the path taken by the Projectile, which is defined as a trajectory. For instance, when a ball is thrown into the air, it will follow a specified trajectory and will fall after a certain point. Because of the gravitational forces, this ball can be considered a projectile.

In the present article, we get an opportunity to present an appreciable depth of information on projectile motion and its various categories. We shall also specifically focus on parabolic motion of projectile and certain projectile motion equations.

## What is a Projectile Motion?

Projectile Motion is defined as a path taken by a particle or object that is thrown indirectly toward the earth’s atmosphere. The object then moves in a curved path, and it faces constant acceleration toward the center of the earth, due to gravitational forces. The path taken by the object is stated as a projectile, and the motion of an object is called Projectile Motion.

There are two simultaneous independent rectilinear motions that we deal in Projectile Motion:

• Along the x-axis: this is a uniform velocity that enables the horizontal or forward movement of any object.
• Along the y-axis: this is uniform acceleration that is triggers downward or vertical movement of the object.

An object and its acceleration in the horizontal projectile motion and vertical projectile motion: When a particle is thrown or shot in the air at a particular pace, acceleration due to gravity becomes the core and the sole force at the moment when it is in the air. This action occurs due to gravity. This acceleration is generally witnessed downward and in a vertical movement. When it comes to horizontal movement, acceleration is absent, inferring the velocity of the object particle when travelling in a horizontal direction stays constant.

## Types of Projectile Motion

There are three types of projectile motions- Oblique Projectile Motion, Horizontal Projectile Motion, and Projectile Motion on an Inclined Plane.

##### Oblique Projectile Motion

When the motion of an object, is Thrown into the air from the ground, the said object is pointed vertically downwards due to the gravitational force acting on it. Then this type of motion is Oblique Projectile Motion.

##### Horizontal Projectile Motion

As the title itself suggests, the projectile motion which acts on a horizontal plane is defined as the Horizontal Projectile Motion.

##### Projectile Motion in Inclined Plane

Similar to the Horizontal projectile motion, the motion of a projectile acting on an inclined plane is stated as the Projectile Motion in an Inclined Plane.

## Parabolic Motion of Projectile

From the above diagram, you can observe that regardless of the angle or inclinational of the projectile, it always results in a parabolic motion. This is mainly because of the gravitational force that acts on it.

### About Parabolic Motion of Projectile

Let us understand the parabolic motion of a projectile by assuming the motion of two objects:

We all are aware of Newton’s law of inertia which states that an object in a horizontal direction will sustain the horizontal movement with the same horizontal speed and direction unless there is an unbalanced horizontal force that affects or alters its movement. The horizontal distance traveled every second denotes a constant value.
In order to arrive at the parabolic motion of a projectile, if we consider two objects where one travels horizontally, and the other is engaged in a vertically accelerated movement, that typifies an object upon which the force of gravity alone casts its influence. When these two motions combine – vertical and horizontal motions, the trajectory formed will be parabolic. Under the parabolic motion of the projectile, the object takes off initially with horizontal velocity where its motion is affected by gravity force, thus sliding down vertically every second forming a parabolic trajectory.

### Projectile Motion Equation

Moreover, in order to calculate different types of parameters, we need to use various types of differential equations of motion or different types of projectile motion equations.

$$v=u-gt$$

$$s=ut- \frac{g t^{2} }{2}$$

$$v^{2} = u^{2} -2gs$$

In which, u = Initial Velocity

g = acceleration due to gravity

v = Final Velocity

s = Displacement

t = Time

### Maximum Height of Projectile

Now that we understand the projectile, its types, projectile motion equations, and most importantly the parabolic motion of the projectile, let us learn about the maximum height of the projectile. Any object’s maximum height of the projectile denotes the peak or the highest vertical position along the trajectory. The horizontal displacement is referred to as the projectile range, which is determined by the initial velocity of a particle.

If v is the initial velocity, g = acceleration due to gravity H = maximum height in meters, θ = angle of the initial velocity from the horizontal plane (radians or degrees).

The maximum height of the projectile is given by the formula:

$$H=2ugsin(2 \theta )$$

## Conclusion

The above article will help you get a complete understanding of Projectile Motion, the equation of trajectory in projectile motion, different types of projectile motions, etc. Now if you have more doubts or you are struggling with any other concepts or chapters in Physics. Then the online interactive classes offered by Tutoroot Platform might help you out. Mainly because with these classes, the students will have expert staff guidance, access to some of the best test books, educational guides, and many more.

## FAQ’s

What is projectile motion?

Projectile Motion is defined as a path taken by a particle or object that is thrown indirectly toward the earth’s atmosphere. The object then moves in a curved path, and it faces constant acceleration toward the center of the earth, due to gravitational forces. The path taken by the object is stated as a projectile, and the motion of an object is called Projectile Motion.

What is Parabolic Motion of the Projectile?

The parabolic motion of a projectile is because of the gravity effect. Gravity leads to projectile taking a curved path and not a straighter one, while down. Since the trajectory is that of a parabola, it is referred to as the parabolic motion of a projectile.

What is the Total Time of Flight?

The time of a flight is measured as the total time consumed to accomplish one projectile motion.  This is twice as much time as the time spent to scale the maximum height.