“Kinematics of projectile motion, for better understanding.

The Kinematics of projectile motion can not be understood without understanding projectile motion. Kinematics is the study of motion without considering the forces responsible for the motion.

Projectile motion referred to the motion of an object that is thrown or launched into the air and moved in a curved path under the influence of gravity. Projectile motion is an important concept in physics, which found its applications in a wide variety of fields including engineering, sports and astronomy.

Kinematics of projectile motion:

The Kinematics of projectile motion can not be understood without understanding projectile motion. Kinematics is the study of motion without considering the forces responsible for the motion.

Projectile motion referred to the motion of an object that is thrown or launched into the air and moved in a curved path under the influence of gravity. Projectile motion is an important concept in physics, which found its applications in a wide variety of fields including engineering, sports and astronomy.

The kinematics of projectile motion is determined by two factors, such as the initial velocity of the projectile and the angle at which it is launched. The initial velocity is the speed and the direction in which the projectile is launched. In contrast, the angle of launch is the angle between the horizontal and the direction of the initial velocity.

Examples of projectile motion include,

• A baseball is being thrown.
• A rocket is being launched into space.
• A bullet is being fired.

The basic principles of projectile motion

Projectile motion can be described using two basic principles of motion such as horizontal motion and vertical motion of an object in projectile motion. Both motions are independent of each other, however, occur simultaneously.

Kinematics of projectile motion: Horizontal motion;

The horizontal motion of a projectile is constant and uniform, which means zero acceleration and constant velocity in a straight line. No force is acting on an object in the horizontal direction, causing the object to move in a straight line unless acted upon by an external force.

Velocity:

The horizontal velocity of a projectile remains constant throughout its motion, as there is no acceleration acting on it in the horizontal direction. Therefore the equation for the horizontal velocity can be written as,

Vx=V₀x

Where,

• Vx is the horizontal velocity at any time.
• V₀x is the initial horizontal velocity of the projectile.

Acceleration:

The horizontal acceleration of a projectile is zero since no external forces are acting on it in this direction. Therefore the equation for horizontal acceleration can be written as,

Ax=0

Where

• Ax is the horizontal acceleration at any time.

Displacement:

The horizontal displacement of a projectile is determined by the initial velocity and the time of flight. Therefore the equation for horizontal displacement can be written as,

Dx=V₀x*t

Where

• Dx is the horizontal displacement at any time.
• V₀x is the initial horizontal velocity of the projectile.
• t is the time of the flight.

The equation for the horizontal motion:

The horizontal motion of a projectile is constant and can be described by the equation;

x=v₀x*t

Where,

• x is the horizontal distance travelled by the projectile.
• v₀x is the initial horizontal velocity of the projectile.
• t is the time elapsed since the projectile is launched.

It is to note that the acceleration of the project in the horizontal direction is zero, hence its velocity throughout the flight remains constant.

Kinematics of projectile motion: Vertical motion;

The vertical motion of a projectile is affected by the gravitational force and follows a parabolic path that causes the object to accelerate downward at the rate of 9.8 meters per second squared (m/s²) near the surface of the earth.  This type of motion is commonly encountered in many areas of physics including mechanics, astronomy and ballistics.

At the same time study of projectile motion is important for understanding a wide range of phenomena including the flight of a baseball to the trajectory of a missile.

Velocity:

The vertical velocity of a projectile changes over time due to the acceleration of gravity. The equation for the vertical velocity can be written as;

Vy=V₀y+gt

Where

• Vy is the vertical velocity at any time.
• V₀y is the initial velocity of the projectile,
• g is the acceleration due to gravity ( which is negative in this case)
• t is the time elapsed.

Acceleration:

The acceleration of a projectile in the vertical direction is only due to the force of gravity and the equation can be written as;

Ay=- g

Where

• Ay is the vertical acceleration at any time.
• g is the acceleration due to gravity.

Displacement:

The vertical displacement of a projectile is also influenced by the acceleration due to gravity. The equation for the vertical displacement can be written as,

Dy=V₀y*t+1/2 gt²

Where,

• Dy is the vertical displacement at any time.
• V₀y is the vertical velocity of the projectile.
• g is the acceleration due to gravity (which is negative).
• t is the time elapsed.

The above equations assume that there is no air resistance for the projectile, only fit for ideal conditions.  

The equation of vertical motion:

The following equation can describe the vertical motion of a projectile;

 y= v₀y*t+(1/2)*a* t² v= v₀y+a*t

where

• y is the vertical distance travelled by the projectile.
• v₀y is the initial vertical velocity of the projectile.
• t is the time elapsed since the start of the projectile’s motion.
• a is the acceleration due to gravity, which is typically taken to be -9.8m/s²(negative because it acts downwards)
• v is the instantaneous velocity of the projectile at any given time during its flight.

It is to be noted that the acceleration due to gravity affects only the vertical motion of the projectile, not the horizontal motion. Also at the maximum height reached by the projectile, its vertical velocity becomes zero, and the time taken to reach this point can be found by setting v=0 as the equation for velocity.

The time flight of a projectile,

The time flight of a projectile is the total time it remains in the air, and can be calculated using the following equation;

 t=2v₀ sin θ / g,

Whereas

• v₀ is the initial velocity,
• θ is the angle of launch,
• g is the acceleration due to gravity.

Height of the projectile

The maximum height of the projectile can be reached that can be calculated using the following equation,

h = v₀² sin²θ / (2g)

Where

• v₀ is the initial velocity of the projectile,
• θ is the angle of launch,
• g is the acceleration due to gravity.

The range of the projectile.

The range of a projectile refers to the horizontal distance that the object travels from its initial point of launch to the point where it hits the ground. This is a measure of how far the object travels in the horizontal direction before it comes to a stop. It can be calculated using the following equation.

R = v₀² sin2θ / g

Where

• R is the range of the projectile,
• v₀ is the initial velocity of the projectile,
• θ is the angle of launch,
• g is the acceleration due to gravity.

Kinematics of projectile motion: Conclusion

Projectile motion can be described using two basic principles of motion: horizontal and vertical motion of an object in projectile motion. The kinematics of projectile motion is determined by two factors, such as the initial velocity of the projectile and the angle at which it is launched.

Both vertical and horizontal motion, velocity, acceleration and displacement are considered and accordingly, equations are derived. The time flight of a projectile, the height of the projectile, and the range of the projectile are calculated on the basis of the equation derived.