Projectile Motion Formula

Introduction

Projectile motion describes the kind of motion that an object possesses when thrown and subjected to the force of gravity. In this regard, a projectile basically can be described in terms of the horizontal and vertical motions separately. Based on these analyses separately, the path the projectile will trace could be predicted.

Formula of Projectile Motion

Following is the formula of projectile motion which is also known as trajectory formula:

Where,

• Vx is the velocity (along the x-axis)

• Vxo is Initial velocity (along the x-axis)

• Vy is the velocity (along the y-axis)

• Vyo is initial velocity (along the y-axis)

• g is the acceleration due to gravity

• t is the time taken

Equations related to the projectile motion, are given as 

 

 

Where

• Vo = initial velocity

• The component along y-axis is sin θ

• The x-axis component is given by cos θ.

The formula of projectile motion gives the computation of velocity, distance, and time involved in the projectile motion of an object.

Solved Problem of Projectile Motion

Problem 1: Jhonson is standing on the top of the building and John is standing down. If Jhonson tosses a ball with a velocity 30 m/s and at the angle of 70° then at the time 3s what height will the ball reach?

Answer:

Given:

Vyo = 30 m/s

Δ t = 3s

 

The vertical velocity in the y-direction is given by

 

Conclusion

Projectile motion is a combination of horizontal and vertical motions in order to describe the trajectory of an object while it's flying. Applying and understanding these integral formulas will enable one to predict the range, maximum height, and time of flight of projectiles. Remember, the first step in solving any projectile problem is to break down the initial velocity into the horizontal and vertical components and apply the appropriate equations.