Free Fall vs. Projectile Motion

Attribute	Free Fall	Projectile Motion
Definition	An object falling under the influence of gravity only.	The motion of an object projected into the air at an angle.
Acceleration	Constant acceleration due to gravity (9.8 m/s^2).	Acceleration due to gravity (9.8 m/s^2) acting vertically and no horizontal acceleration.
Path	Straight line vertically downwards.	Parabolic trajectory.
Initial Velocity	Can be zero or non-zero.	Non-zero and can have both horizontal and vertical components.
Angle of Projection	N/A	Can be any angle between 0 and 90 degrees.
Time of Flight	Depends on the height from which the object is dropped.	Depends on the initial velocity and angle of projection.
Maximum Height	N/A	Depends on the initial velocity and angle of projection.
Range	N/A	Depends on the initial velocity and angle of projection.
Vertical Velocity	Increases in magnitude as the object falls.	Changes continuously due to the effect of gravity.
Horizontal Velocity	Zero.	Remains constant throughout the motion.

Introduction

Physics is a fascinating subject that helps us understand the fundamental laws governing the motion of objects. Two important concepts in physics are free fall and projectile motion. While both involve the motion of objects in the presence of gravity, they have distinct attributes that set them apart. In this article, we will explore the characteristics of free fall and projectile motion, highlighting their similarities and differences.

Free Fall

Free fall refers to the motion of an object under the sole influence of gravity, with no other forces acting upon it. In free fall, an object is subject to a constant acceleration due to gravity, which is approximately 9.8 m/s² near the surface of the Earth. One key attribute of free fall is that all objects, regardless of their mass, fall with the same acceleration. This means that if two objects are dropped from the same height, they will hit the ground at the same time, neglecting air resistance.

Another important characteristic of free fall is that the velocity of the object increases linearly with time. This means that the object's speed increases by the same amount every second. For example, if an object is in free fall for 2 seconds, its velocity will be twice the acceleration due to gravity. The distance traveled by an object in free fall is directly proportional to the square of the time elapsed since it was released.

Furthermore, during free fall, the object experiences a downward force equal to its weight. This force is responsible for the object's acceleration. As the object falls, its weight remains constant, but the force exerted by the air resistance increases, eventually reaching a point where it balances the weight, resulting in a constant velocity known as terminal velocity.

In summary, free fall involves the motion of an object solely under the influence of gravity, with a constant acceleration, equal velocities for all objects regardless of mass, and a distance traveled proportional to the square of time.

Projectile Motion

Projectile motion, on the other hand, refers to the motion of an object that is launched into the air and moves along a curved path under the influence of gravity. Unlike free fall, projectile motion involves an initial velocity imparted to the object, which gives it both horizontal and vertical components of motion.

One key attribute of projectile motion is that the horizontal component of velocity remains constant throughout the motion. This means that the object's horizontal speed does not change, regardless of the object's vertical motion. As a result, the object travels equal horizontal distances in equal time intervals, neglecting air resistance.

Another important characteristic of projectile motion is that the vertical component of velocity changes due to the acceleration of gravity. As the object moves upward, its vertical velocity decreases until it reaches its maximum height, where the velocity becomes zero. On the way down, the velocity increases in the opposite direction until it reaches the same magnitude as the initial velocity.

Furthermore, the path followed by a projectile is a parabola. The shape of the parabolic trajectory depends on the initial velocity and launch angle. The range, or horizontal distance traveled by the projectile, is maximized when the launch angle is 45 degrees. Additionally, the time of flight, or the total time the projectile is in the air, is determined by the initial velocity and the launch angle.

In summary, projectile motion involves the motion of an object launched into the air, with both horizontal and vertical components of velocity, a constant horizontal velocity, a parabolic trajectory, and a range and time of flight determined by the initial velocity and launch angle.

Similarities and Differences

While free fall and projectile motion both involve the motion of objects under the influence of gravity, they have distinct attributes that differentiate them. One key similarity is that both free fall and projectile motion experience the same acceleration due to gravity. However, in free fall, the object starts from rest, while in projectile motion, the object has an initial velocity.

Another similarity is that both free fall and projectile motion follow a curved path. In free fall, the path is a straight line vertically downward, while in projectile motion, the path is a parabola. However, the shape of the parabolic trajectory in projectile motion depends on the initial velocity and launch angle.

Furthermore, both free fall and projectile motion involve the concept of time. In free fall, the distance traveled is directly proportional to the square of the time elapsed, while in projectile motion, the time of flight is determined by the initial velocity and launch angle.

However, a key difference between free fall and projectile motion is that in free fall, the object's motion is solely influenced by gravity, while in projectile motion, the object has an initial velocity that affects its motion. Additionally, in free fall, all objects fall with the same acceleration, while in projectile motion, the horizontal component of velocity remains constant.

Moreover, free fall is a special case of projectile motion, where the initial velocity is zero. This means that free fall can be considered as a subset of projectile motion, with specific conditions.

Conclusion

Free fall and projectile motion are two important concepts in physics that involve the motion of objects under the influence of gravity. While free fall refers to the motion of an object solely influenced by gravity, projectile motion involves an object launched into the air with an initial velocity. Both free fall and projectile motion have similarities, such as following a curved path and being influenced by the acceleration due to gravity. However, they also have distinct attributes, including the presence of an initial velocity in projectile motion and the constant acceleration for all objects in free fall. Understanding these concepts helps us comprehend the fundamental principles of motion and gravity in the world around us.