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Projectile motion encompasses the two-dimensional movement of objects launched into the air, influenced solely by gravity. This motion can be horizontal or angled, with distinct trajectories. Understanding its fundamentals involves analyzing horizontal and vertical displacements, time of flight, range, and maximum height. These concepts are pivotal in fields like ballistics and engineering, where predicting a projectile's path is crucial.

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## Definition of Projectile Motion

### Kinematics

Projectile motion is a type of kinematics that describes the motion of an object subject only to the acceleration due to gravity

### Trajectory

The motion of a projectile follows a two-dimensional curved path known as a trajectory

### Factors Affecting Projectile Motion

The trajectory and behavior of a projectile are determined by its initial velocity, angle of launch, and acceleration due to gravity

## Types of Projectile Motion

### Horizontal Projectile Motion

Horizontal projectile motion occurs when an object is launched with an initial velocity parallel to the Earth's surface

### Angled Projectile Motion

Angled projectile motion involves launching an object at an angle to the horizontal, resulting in an asymmetric trajectory

### Analysis of Projectile Motion

The analysis of both types of projectile motion involves decomposing the motion into horizontal and vertical components and applying the principles of kinematics

## Equations and Metrics of Projectile Motion

### Horizontal Displacement

The horizontal displacement of a projectile can be calculated using the equation x = vx * t, where vx is the horizontal component of the initial velocity

### Vertical Displacement

The vertical displacement of a projectile can be calculated using the equation y = vy * t - (1/2) * g * t², taking into account the effects of gravity

### Time of Flight, Range, and Maximum Height

Key metrics in projectile motion include the time of flight, range, and maximum height, which can be calculated using specific equations

## Vector Analysis of Projectile Motion

### Vector Quantities

The initial velocity, gravitational acceleration, and displacement in projectile motion are vector quantities with horizontal and vertical components

### Vector Equations

Vector equations for displacement and velocity can be used to determine the position and velocity vectors of a projectile at any point in time

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