Introduction to Projectile Motion

What is Projectile Motion? Well, it is the motion of a projectile, such as a thrown ball, an arrow, or a baseball, concerning the force of gravity and masses of the projectile and the earth. Given the initial velocity and angle of projection, it is a problem that has been studied since ancient times. The solution is not obvious and can be approached in various ways. Galileo was one of the first people to have ever described projectile motion This article will go through a basic introduction of Projectile Motion, it’s important terms and definitions, projectile motion equations, applications, and formulas.

What is Projectile Motion?

The Projectile in physics refers to an object that is in flight after being thrown or projected. In a projectile motion, the only acceleration acting upon is the acceleration due to gravity. Therefore, equations of motion can be applied separately at the X-axis and Y-axis to find the unknown parameters.

The path of a projectile can be discussed in two ways. One part of the path is horizontal, where there is no acceleration. The other part of the path, however, is vertical and constant – this part is due to gravity. For example, you might think about a football or cricket ball being thrown up in the air, traveling along its curved path before landing back down on earth.

Some Important Terms

• The angle of Projection: The angle at which the body is projected concerning its horizontal position is called the angle of projection.

• The velocity of Projection: The velocity with which the body is thrown is called the velocity of projection.

• Point of Projection: The point from which the body is projected in the air is called the point of projection.

• Projectile Trajectory: The path taken by a projectile in the air is called a projectile trajectory.

• Horizontal Range: The horizontal distance traveled by the body performing projectile motion is the range of the projectile.

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= 12mu2

• At the lowest point, Linear momentum= mu

• Acceleration of projectile acts vertically downwards being equal to g and is constant throughout the motion.

• Angular momentum of a projectile = m u cosθ h, where h is the height.

• The angle between velocity and acceleration varies from 0° < θ < 180°, in the case of angular projection.

• The maximum height occurs when the projectile covers a horizontal distance that is equal to half of the horizontal range, i.e., R/2.

• When the maximum range of the projectile is R, at that moment its maximum height will be R/4.

Important Formula Related to Projectile

Projectile Motion Application

• Throwing a ball or anything: 

When a ball is thrown up into the air, we see that it travels for some distance and then falls. This path followed by the object appears to be like a parabola or U-shaped curve. This part of the path is neither linear nor circular; it is called projectile motion, and the path followed by the ball or the object is called its trajectory. So, when we throw a ball horizontally into the air, it does a loop that goes up and over as if going in a parabola-like pattern and then comes back down. This happens because of projectile motion. In physics, particularly mechanics (the study of physical change), an object’s speed is calculated by dividing its distance from an observer by how much time has passed; if an object covers 30 meters in two seconds, then it has been traveling at 15 meters per second (15 m/s). This business applies to any kind of force exerted on an object since all forces produce changes in motion or state of motion.

• Bullet fired from a gun:  

When an object is propelled through the air, numerous forces are acting on it simultaneously. The force from the ignition of gunpowder and the force of gravity combine to influence how long and in what direction the bullet travels. However, as soon as the bullet leaves the gun, gravity begins to exert a greater force and begins guiding it toward earth whether it falls or not depends entirely on how much opposing force is met along its path.

Projectile Motion Example

A projectile is projected from point Q at an angle of 30° with an initial velocity of 30 m/s. The projectile hits the ground at M. (Note that g = 10m/s2) Then find following v:

1. Total time of flight
2. Horizontal Range of the projectile (QM)
3. Maximum height of the projectile

Solution:

Initial velocity u = 30m/s.

The angle of projection, θ = 30°.

1. Time of flight

T = 2u sin g

Putting the given values,   

T = (2 × 30 sin 30°)/10 

  = 3 s

2. Horizontal Range

R = u2 sin 2g

Putting the values we get,     

R = [(30)2 sin 60°]/10

   = 45 √3 m.

3. Maximum Height

H = u2 sin22g

Putting the values,    

H  = [(30)2sin2(30°)]/ (2 × 10)

        = 11.25 m.

Conclusion

The projectile in physics refers to an object that is in flight after being thrown or projected. In this article, we 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.