Understanding Projectile Motion

Expert reviewed • 22 November 2024 • 7 minute read

What is Projectile Motion?

Projectile motion is a type of two-dimensional motion that combines horizontal and vertical components. The key to analysing projectile motion lies in treating these components independently:

Horizontal Motion: In the absence of air resistance, the horizontal component of motion experiences no acceleration. This means the horizontal velocity remains constant throughout the projectile’s flight.
Vertical Motion: The vertical component is subject to a constant acceleration due to gravity, which on Earth is approximately 9.8 m/s² downward.

Galileo’s Groundbreaking Analysis

Galileo Galilei, the renowned Italian physicist, was the first to accurately describe the path of a projectile as parabolic. His analysis forms the foundation of our modern understanding of projectile motion.

Key Principles of Galileo’s Analysis:

The path of a projectile forms a parabola.
Horizontal and vertical motions are independent of each other.
Gravity acts only on the vertical component of motion.

Velocity Components in Projectile Motion

Understanding the behaviour of velocity components is crucial for analysing projectile motion:

Horizontal Velocity $(v_x)$ :
- Remains constant throughout the motion (assuming no air resistance).
- $v_x = vcos (θ)$ , where $v$ is the initial velocity and $\theta$ is the launch angle.
Vertical Velocity $(v_y)$ :
- Changes continuously due to gravity.
- Initial vertical velocity: $v_y = vsin (θ)$
- At any time $t:v_y=vsin(θ)−gt$ , where $g$ is the acceleration due to gravity.

What are Important Equations for Projectile Motion?

To analyse projectile motion, we use a set of equations known as the "SUVAT" equations. Here are the key equations adapted for projectile motion:

For horizontal motion:

x=v_0cos(θ)t

v_x=v_0cos (θ)

For vertical motion:

y = v_0 \sin(\theta) t - \frac{1}{2}gt^2

v_y=v_0sin(θ)−gt

Where:

$x$ and $y$ are horizontal and vertical displacements
$v_0$ is initial velocity
$\theta$ is launch angle
$t$ is time
$g$ is acceleration due to gravity (9.8 m/s² downward on Earth)

Key Points to Remember

Projectile motion combines constant horizontal velocity with accelerating vertical motion.
The path of a projectile forms a parabola in the absence of air resistance.
Horizontal and vertical components of motion are independent.
Gravity only affects the vertical component of motion.
The velocity vector changes continuously in direction and magnitude, except at the highest point where it’s purely horizontal.

What are Important Assumptions Used in Projectile Motion?

When analysing projectile motion, especially in introductory physics, we make several simplifying assumptions:

Air resistance is negligible.
The acceleration due to gravity is constant and uniform.
The curvature and rotation of the Earth are negligible for short-range projectiles.

These assumptions allow for simpler calculations but it’s important to remember that real-world projectile motion often deviates from this idealised model due to factors like air resistance and variations in gravitational field strength.

Up Next

Initial Velocity and Launch Angle

Return to Module 5: Advanced Mechanics