Machines Theory

Understanding projectile motion

An object or particle (referred to as a projectile) is launched close to the surface of the earth, where it moves along a curved path only under the influence of gravity. The only significant force acting on the object is gravity, which pulls it downward and accelerates it in that path.  The motion can be broken down into two parts. The horizontal component of the velocity, ucos, remains constant if u is the initial velocity at some angle. Gravity causes the vertical component, usin, to accelerate, and it evolves over time. This acceleration is constant at every point of flight. well In this post, you’ll get to learn the definition, types, examples, equations, and some calculations of projectile motion.

Projectile motion

What does projectile mean?

Any object that is thrown or fired into the air and is only influenced by gravity afterwards is referred to as a projectile. An object needs to be given some initial force before it can become a projectile. Projectiles include things like a diver jumping from a diving board, a cannonball fired from a cannon, and a baseball that is being hit by a batter. The force exerted by the bat, cannon, or diving board causes the object to move in a projectile motion.

Projectile motion

What is projectile motion?

Projectile motion, which simply depends on the initial speed, the launch angle, and the acceleration due to gravity, describes the trajectory of the projectile. A trajectory is the path that an object takes after being launched. The speed an object is moving at when it is initially launched into the air is known as its initial speed or velocity. The angle at which an object is launched is referred to as the launch angle. The maximum height, range, and flight duration of a baseball are all determined by its speed and angle at the moment it leaves the bat.

An object that has been projected or thrown into the air is referred to as a projectile. The only acceleration present in projectile motion occurs vertically and is caused by gravity (g). Equations of motion can be applied separately in the X- and Y-axes to determine the unknown parameters. The only factors affecting an object’s predictable path are its initial launch speed, launch angle, and gravitational acceleration.

From your current sitting position, you can test it out. Grab something and throw it up and away from you with care. As it flies away from you, it will ascend to its highest point before starting to descend to the ground. While you’re at it, throw some more items. The projectile paths ought to be comparable as long as you’re not throwing paper or feathers.

Read more: Understanding distance and displacement

Types of projectile motion

These are the three types of projectile motion

  • Oblique projectile motion.
  • Horizontal projectile motion.
  • Projectile motion on an inclined plane.

Oblique projectile motion

Speed, velocity, vertical component of velocity (u sin), momentum, kinetic energy, and potential energy all change in oblique projectile motion, but the horizontal component of velocity (u cos), acceleration (g), and mechanical energy remain constant. Velocity and KE are at their highest at the projection point and at their lowest (but not zero) point, accordingly.

Horizontal projectile motion

When a body is launched horizontally with initial velocity u from a height ‘y’ vertically above the ground. There cannot be any additional horizontal force acting on the horizontal motion if friction is considered to be absent. As a result, the object’s horizontal velocity remains constant, covering an equal amount of ground in an equal amount of time.

Projectile motion on an inclined plane

Projectile Motion on an Inclined Plane describes the motion of a particle projected up from an inclined plane at a speed u that forms an angle with the inclined plane and the horizontal velocity of projection. Kshetrapal, (2013).

Read more: Understanding Free Fall

Examples of projectile motion

Below are a few examples of projectile motion.

Shooting a basketball
Shooting a basketball
Throwing a baseball
Throwing a baseball
Javelin throw
Javelin throw
Hitting a golf ball
Hitting a golf ball
Kicking a football
Kicking a football
Playing a tennis ball
Playing a tennis ball

Read more: Understanding kinematics

Projectile motion equations

Here are the equations of projectile motion:

Projectile motion equations

Projectile motion equations

Projectile motion equations

Projectile motion equations

Projectile motion equations

Projectile motion equations

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Projectile motion equation

Where,

  • Vy is the velocity (along the y-axis)
  • Vx  is the velocity (along the x-axis)
  • Vyo is initial velocity (along the y-axis)
  • Vxo is Initial velocity (along the x-axis)
  • Vo is the initial velocity
  • sin θ is the component along the y-axis
  • t is the time taken
  • g is the acceleration due to gravity

Read more: Understanding acceleration

Basketball physics

We are aware that two-dimensional motion, or motion on a plane, is a sort of projectile motion. It is believed that the force of gravity is the only force acting on a projectile (the thing moving as a projectile). But in the real world, how do we define projectile motion? What practical applications can be made of the concepts of projectile motion?

Let’s look at some actual instances of two-dimensional projectile motion. We are all familiar with basketball. To make a basket, the player makes a small jump and puts the ball into the hoop. The ball moves in the form of a projectile. Therefore, it is known as projectile motion.

What benefit does jumping have for the probability of making a basket? Aside from basketball, all motions have one thing in common, whether it be throwing a cricket ball, a stone into a river, a javelin, an angry bird, a football, or a bullet.

Each one exhibits a projectile motion. And that is that gravity is the only force acting on them after they are released. As a result, everyone of them experiences an equal and impartial downward pull.

It means that predicting how long a projectile will stay in the air and how far it will travel before hitting the ground is simple. There wouldn’t be any horizontal acceleration if the air resistance was disregarded. This shows that a body can be considered to be moving in two dimensions with just one direction of acceleration, as long as it is thrown close to the surface.

However, how is it possible to say that a body launched into the air moves in a two-dimensional way? Let’s assume a ball is rolling as illustrated below to help us understand this:

Basketball physics

What can we say about the dimension of motion now that the ball has been moved along the path illustrated? The most typical response would be that, since it is travelling on a plane and has both an x-component and a y-component, it must be an instance of motion in two dimensions.

However, it is incorrect because a line that can perfectly define the motion of the basketball already exists. It is an illustration of one-dimensional motion as a result. The motion’s actual nature is therefore unchanged by the axis choice.

Basketball physics

The ball’s velocity now includes three components: an x component, a y component, and a z component if it is thrown at the angle illustrated.

Does this indicate that the motion is three-dimensional? Here, it is clear that a plane, not a line, can define such a motion. As a result, there is a plane that completely captures the motion of every body launched at any angle.

Thus, it can be concluded that no matter how the axes are chosen, a body’s motion will only be in two dimensions if it is close to the Earth’s surface and the influence of air resistance can be ignored.

The motion of the ball can be defined clearly by and if the axes are rotated in this way, as shown below:

Basketball physics

Therefore, it can be said that the dimension of a body’s motion is totally determined by the minimum number of coordinates necessary to define it.

Read more: Understanding gravitational energy

Calculations

Here are a few examples, as well as solutions for projectile motion.

Example 1

A projectile with a velocity of 300ms–¹ is fired from the ground level at a 30° angle to the horizontal. Calculate the time taken to reach the maximum height?

Solution

Taking g to be 10ms-²

Projectile motion solution

Read more: Forms of energy: kinetic and potential energy

Example 2

Example 2

Solution

Solution

FAQs

What is projectile motion?

Projectile motion, which simply depends on the initial speed, the launch angle, and the acceleration due to gravity, describes the trajectory of the projectile. A trajectory is the path that an object takes after being launched. The speed an object is moving at when it is initially launched into the air is known as its initial speed or velocity.

What are the 3 types of projectile motion?

  1. Oblique projectile motion.
  2. Horizontal projectile motion.
  3. Projectile motion on an inclined plane.

What are four examples of projectile motion?

  • Shooting a basketball.
  • Throwing a baseball.
  • Shooting an arrow.
  • Javelin throw.

What is projectile motion and its formula?

A projectile travels in a parabolic path. The projectile’s acceleration, which acts vertically downward and is constant during the motion, is equal to g. Projectile angular momentum is equal to mu cos h, where h stands for height.

What is a projectile with examples?

Any object that is cast, fired, launched, heaved, hurled, pitched, tossed, or thrown is referred to as a projectile. Projectile motion is illustrated by actions like throwing a ball straight up, kicking a ball and giving it speed at an angle to the horizontal, or just dropping something and letting it fall freely.

What is the angle of projection?

The projection angle is the angle made between the projection direction and the horizontal drawn at that point.

What is the velocity of a projectile?

A projectile always moves horizontally at the same speed (a constant change in value). Gravity causes a downward vertical acceleration with a magnitude of 9.8 m/s per second. A projectile’s vertical velocity changes by 9.8 m/s per second. A projectile’s vertical motion is unrelated to its horizontal motion. The projection velocity is the least speed necessary to launch an object vertically up to a certain height.

What is the maximum height of a projectile?

  • The equation for the maximum height of a projectile is H = u 2 sin 2 θ 2 g.

That is all for this article, where the definition, types, examples, equations, and some calculations of projectile motion have been discussed.

I hope you learn a lot from reading this post. If you do, kindly share it with your other mates. Thanks for reading, see you around!