Uniform Acceleration – Projectile Motion

As the name suggests, projectile motion is the movement of an object that is launched into the air. The object is referred to as the projectile, and the path travelled by it is referred to as its trajectory. After the initial force propels the object into the air, the object experiences gravity and is also subjected to frictional force. These cause it to slow down. However, calculating the frictional force, also known as air resistance, is often complex and hence is left out at the beginner level. 

Types of motion

Based on the cartesian system, there are three types of motion.

1. One-dimensional motion that occurs along a single axis, X, Y, or Z.
2. Two-dimensional motion that happens along a plane like XY, YZ, and ZX.
3. Three-dimensional motion, which happens in most cases involving coordinates of all the three axes.

Even though there are three main motion types, in the kinematics equations, we consider the single dimension motion only. For two-dimensional motions, projectile motion is the best example.

What is uniform accelerated motion?

To solve the uniform accelerated motion problem, we must first define what a uniform accelerated motion is. As the name implies, the item or frame is moving in a uniformly accelerating manner with a constant acceleration. Constant acceleration does not imply that you are moving at a standstill. As a result, the concept of uniform acceleration or uniform acceleration definition indicates that if a frame is below movement, the quantity of alternation in its pace in the same time intervals will be constant.

In other words, a uniform acceleration motion occurs when an object moves in a straight line and its rate of change over some time period is constant. We can see the uniform acceleration in a direct line movement because of the consistently elevated movement.

Now, some more extreme examples of uniform acceleration are listed below:

1. A ball is rolling down a hill.
2. When a cyclist uses their bicycle on a slope.
3. Sliding down the slide.

Uniform Acceleration Equations

For uniform acceleration, the equation of motion is as follows:

The velocity equation is as follows:

In terms of displacement, we have another equation for velocity:

Equations of free-fall motion under gravity

When a body freely falls from a height, its motion is controlled by the acceleration due to gravity or g, whose value is considered as 9.8 ms⁻² on earth. In such cases, displacement S is replaced by height h in the kinematics formulas.

v = u + gt ……. (7)

h = ut + (½)gt² ……. (8)

v² = u² + 2gh ……. (9)

If the body moves against the acceleration due to gravity, like a ball being thrown in the upward direction or someone climbing a ladder, to explain the kinematic equation for uniformly accelerated motion, the (-g) is considered in the form of (+g).

Parabolic Motion of Projectiles

A movement in dimensions is also referred to as motion in an aircraft—circular Motion, Projectile Motion, etc. The reference factor for evaluating this type of movement (i.e., Projectile Motion) might be the product of a foundation and the two coordinate axes X and Y. Projectile movement is one of the most common instances of movement in an aeroplane.

A projectile is an object that has been thrown or projected and is now in flight. The simplest acceleration in a projectile movement occurs inside the vertical trajectory, which is due to gravity (g). To discover the unknown parameters, equations of movement can be implemented one at a time in the X-axis and Y-axis.

A projectile is an object that has been thrown or projected and is now in flight. The simplest acceleration in a projectile movement occurs inside the vertical trajectory, which is the acceleration due to gravity (g). To discover the unknown parameters, equations of movement can be implemented one at a time in the X-axis and Y-axis.

Football, baseball, cricket ball, and other items are instances of projectile motion. The projectile movement is divided into a horizontal movement with no acceleration and a vertical movement with constant acceleration due to gravity. The movement of the projectile is normally in the shape of a parabola, which is represented as

In order to simplify the computations, projectile movement is computed without taking into account air resistance. The movement of an object below the force of gravity is depicted in the diagram above. It’s an example of projectile motion (a unique plane movement case). As a result, the movement of a projectile is taken into account:

A Few Two-Dimensional Projectile Examples

• Throwing a ball or a cannonball. 
• At a billiard table, the movement of a billiard ball.
• The movement of a shell after it has been fired from a gun.
• A ship’s movement in a river.
• The earth’s rotation around the sun.

Important Points Related to Projectile Motion

• At the highest point, linear momentum is m(u cos θ), and the kinetic energy is  12m(u cosθ)².

• The projectile has a parabolic path.

• At the lowest point, Kinetic energy = 1/2mu²

• At the lowest point, Linear momentum = mu

Important Formula Related to Projectile

Conclusion

The projectile in physics refers to an object in flight after being thrown or projected. This article covered the Introduction of Projectile Motion, its definition, the various important terms you need to know, some very important points related to projectile motion, some important formulas, and lastly, the real-life application of Projectiles.