Projectile Motion

By Pratik Choudhury

(Test Preparation (ACT/SAT/SSAT), IGCSE/MYP Math & Physics, IB Physics tutor at The Edge Learning Center)

Any object projected at an angle is said to be a projectile and the motion it undertakes is known as projectile motion, which is two-dimensional.

Our study of the motion of a free-falling object through general observation – a motion caused due to gravity – helps us to analyse the motion of a projectile. As a result, we tend to think that projectile motion is similar to that of the motion of a free falling object, but that’s only partially true. There is more to it.

In theory, an object projected into space has two simultaneous motions – each totally independent of the other. People of great astuteness have denied the simultaneous motions of a projectile for centuries. In fact, in the early days of science, in particular during the era of gunpowder, it was argued that that an object fired from a canon had two distinct motions. First, the object would undergo a motion resulting from the explosion of the gunpowder and then it will fall to the ground due to natural motion. In other words, the cannonball would move in the direction it was fired until the gunpowder’s effect had ceased and eventually fall straight back to Earth.

Galileo Galilei

It was actually Galileo, who gave the first correct insight to two-dimensional motion. He proposed the idea of constant velocity and constant acceleration, which at that point in time was quite contradictory. How can an object under the influence of constant acceleration have constant velocity? It was a conundrum!!! However, he proved that the force of the gunpowder was applied only at the instant of the explosion, and that instantaneous force resulted in giving the ball constant horizontal velocity. To think of it, if air resistance is negligible and there is no force opposing the horizontal motion of the cannonball then the cannonball will land with the same speed at a certain distance (depending on the angle at which it is projected) away from the canon.

According to Newton’s First Law of Motion, if an object is projected at a constant velocity and there are no other external forces aiding or opposing its motion then it will continue to travel in a straight line for as long as it takes. The same law is also applicable in case of a projectile motion; however, in this case there is ‘an external force’ and that force happens to be ‘force due to gravity’. As such, as soon as the ball leaves the canon, force of gravity will try to accelerate the ball back to earth at a constant rate of .

Acceleration due to gravity is the only acceleration experienced by a projectile and it plays a role only in its vertical movement. Since there is no acceleration abetting its horizontal movement and there is no air resistance (negligible), so the horizontal velocity does not change during its entire flight. The horizontal velocity after 1 second of launch will be the same as the horizontal velocity 5 seconds later.

The component of the constant velocity, which is responsible for driving the projectile upwards, is known as Vertical Component (y-component) and the component, which is responsible for its lateral movement, is known as Horizontal Component (x-component). Both the components can easily be computed through simple trigonometric calculation.

Another important aspect of a projectile motion is the path or the trajectory of the object. The trajectory of a projectile is curved or parabolic. This curved path is due to the object’s constant horizontal velocity and its changing vertical velocity.

projectile motion

Note that the length of the horizontal component vector is the same, but the length of the vertical component vector changes during the flight’s duration.

One more important feature of a projectile motion is the amount of time a projectile takes to get to the top of its trajectory. The time taken to reach to the top is same as the time taken to return back to the exact height from where it was launched.