Projectile Motion

What is Projectile Motion - Definition & Formula

We all know from Newton’s Universal Laws of Gravity that any object on Earth is constantly influenced by gravity and pulled towards the center of the gravitational field, that is the center of the Earth. Gravity influences any object suspended in the air to fall downwards, as in the case of fruits from trees. Also, if you launch an object up into the air, it travels into the air due to its inertia of motion. But since the object is also under the influence of gravity, it also dips down in the ground. Due to the influence of gravity, that object takes a curve path forward towards the ground before it eventually stops after touching the ground. The object which is launched into the air is called projectile, and this kind of motion is called projectile motion.
When we throw an object up, due to the force of gravity it eventually comes down. An object which is in motion in the air with no other force but gravity influencing it is a projectile. We can define projectile as an object which is projected into the air with only downward gravitational force influencing it and continues its motion by the virtue of its own inertia.

 Projectiles can roughly be classified into three kinds

  • 1) A projectile which is left to free fall from a considerable height

  • 2) A projectile which is launched directly upwards

  • 3) A projectile upwards at an angle towards the horizontal

  • Projectile motion is the motion experienced by an object in the air only under the influence of gravity. A projectile, that is launched into the air near the surface of the Earth’s and moves along a curved path, or in other words a parabolic path, under the action of gravity, assuming the air resistance is negligible. Study of such motion is called ballistics. The only force acting upon a projectile being gravity, which imparts a downward acceleration to the projectile. Because of the object’s initial inertia, an external force in unnecessary to maintain the horizontal velocity of the object. It also requires considering other external forces like friction from aerodynamical drag or internal propulsion when the projectile motion is at a larger scale.

    Ballistics, the study of projectile motion:


    The science of mechanics that deals with the flight, behaviour, and effects of projectiles are called ballistics. The word ballistics comes from the word ballista, which was a siege machine used for war during the late 18th century. Ballista was a weapon that is used to hurl boulders or spears against the enemy troops or walls. The boulder or spears used against the enemy was launched by the ballista, after which it would travel in a parabolic path and land among the enemy. The operators of the ballista have to be concerned about the angle to launch the projectile and the path they had to travel to gauge the landing position of the ballista. This is the reason the study of projectile motion is called ballistics. The path travelled by the projectile after it is launched is called the ballistic trajectory. The study of ballistics is important in modern warfare since it involves calculating the trajectories of modern warfare equipment like bullets, unguided bombs, rockets, and such other equipment. It also involves the designing of projectiles to attain desired acceleration and performance.

    The elementary equations of ballistics only take into account the initial velocity of the projectile and an assumed constant gravitational acceleration. Practical applications of ballistics have to consider a variety of other factors like air resistance, crosswinds, target motion, the varying acceleration due to gravity, and in the case the target is significantly far away, even the rotation of the earth.

    The weapon with the highest potential for destruction is named the ballistic missile since it involves delivering warheads to a target by a missile which follows a ballistic trajectory and falls on the target under the influence of gravity.

    Key components which are to be remembered while dealing with projectile motion:



    In the given diagram

    The key components which we should remember when calculating projectile motion and solving problems are

  • • Initial launch angle, or angle of projection θ

  • • The initial angle of projection varies from 0° to 90° And it heavily influences the motion of a projectile.

  • • Initial velocity, u

  • If the path of the projectile, its launching point, and its target is plotted on a graph, initial velocity can be expressed as x and y components. The initial velocity of the projectile, in that case, can be given as

    ux = u⋅cosθ= or uy = u⋅sinθ
     or we can use the Pythagoras theorem to find the velocity
    u=
  • • Time of flight, T

  • The time of flight is the time period from when the object is launched to the time it reaches the ground. The time period the projectile is in the air depends on the initial velocity and the angle of projection. It is given as

    T = or 

    Acceleration, a

    There is no acceleration in the horizontal direction in case of projectile motion. The only acceleration present is the downward acceleration, that is acceleration due to gravity, also known as free fall. It is given as

    ax = 0 or ay = -g

    The value of g is equal to 9.8 m/s

  • • Horizontal velocity, ux, and Vertical velocity, uy

  • At any point in the projectile motion, the horizontal velocity remains constant. On the other hand, vertical velocity varies linearly. This is because acceleration is constant at 9.8 m/s

  • • Displacement, d or position at time t

  • At time given by t, the displacement components in a graph plotted with the origin of the projectile as the origin, the displacement components are

    X = u.t.cosθ and y = u.t.sinθ- gt2


  • • Maximum height, H

  • The maximum height of the projectile is the highest height the projectile can reach
    It is given by
    H =
    Range, R
    The range of a projectile is the distance between the launch point and the target in a straight line.
    It is calculated by
    R =