Kinematics-Projectile Motion-Path of a projectile

The projectile motion refers to throwing or projecting an object into the air so that it is subject only to gravity. There are several applications of projectile motion in the fields of engineering and physics. Some examples of projectile motion are ball motion in a sports game, entry of meteors in our planet’s atmosphere, and fireworks. Such objects are known as projectiles, and they follow a certain path. This path of a projectile is known by experts as a trajectory. Keep on reading to learn about the path of a projectile in detail. 

What is projectile motion?

The projectile motion refers to an object’s motion, whose projection takes place into the air. After the initial launching force, the object only undergoes the gravity force. The path that this object follows is known by scientists as a trajectory. While travelling through the air, a frictional force pertaining to air resistance will act on the object.

Every object would encounter air resistance on our planet. Because of this, the motion slows down and stops after some time. In calculations of physics, air resistance is generally ignored.

A projectile refers to any object whose launching takes place into the air such that it is affected by the force of gravity. For an object to qualify as a projectile, an initial force must create an impact on it. Some common real-life examples are a diver who jumps, a cannonball that is fired, and a cricket ball that gets hit. In these cases, you will notice that there has been an application of some force.

Some examples of projectile motion are a golf ball that is struck and a baseball that is hit by a bat. In these cases, the projection of a projectile takes place with a certain amount of force. This force takes place at a certain angle to a direction that is vertical. The force responsible for initiating motion is known by experts as a contact force. Once the motion of the ball is initiated, the role of contact force comes to an end. It does not have a subsequent impact on the ball’s velocity as the contact is lost.

The formula of the path of a projectile

Suppose the projection of a projectile of mass ‘m’ takes place with velocity ‘u’ at an angle θ with the ground. Here, the initial velocity’s horizontal component is ux = u cosθ. An important point to note is that it remains constant. The horizontal displacement at any time ‘t’ can be represented as,

x = ux x t = ut cosθ

 ⇒ t = x/(u cosθ) 

The vertical component is represented by, uy = u sinθ 

The vertical displacement at any particular time ‘t’ can be expressed as, 

y = uyt – ½ gt2 = ut sinθ – ½ gt2

y = u[x/u cosθ] sinθ – ½ g[x/(u cosθ)]2

y = x tanθ – gx2 /[2u2cos2 θ]

This gives us the equation of the path of a projectile that happens to be parabolic in nature.

Important points to keep in mind when analysing the path of a projectile

Keep in mind the following important points regarding the path of a projectile.

• Make sure to resolve the motion’s two components: vertical and horizontal. This should be done along the x and y-axes. 
• The motion should be treated as two independent one-dimensional motions. One is vertical motion and the other, of course, is horizontal. Now, make use of the kinematic equations for the vertical and horizontal motions
• Solve the unknowns in the horizontal motion and the vertical motion separately. Time t must be the only common variable between the motions. 
• Finally, a recombination of the various quantities in the horizontal and vertical directions must happen. This would give us the value of the total velocity and displacement.

Conclusion

The projectile motion refers to the motion of throwing an object into the air such that it is subject only to gravity acceleration. Such objects are known as projectiles, and they follow a certain path of motion. This path of a projectile is known in physics as trajectory. To understand this path well enough, you must first learn about the fundamentals of projectile motion. There is also a formula for this path which you must learn as well as its derivation. Finally, you should learn some important points to keep in mind when analysing this motion’s path.