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Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity, following a curved path known as a trajectory. This type of motion can be analyzed as a combination of two independent motions: horizontal motion and vertical motion.

▎Key Characteristics of Projectile Motion:

1. Independence of Motion:
- The horizontal and vertical components of motion are independent of each other.
- The horizontal motion is uniform (constant velocity), while the vertical motion is uniformly accelerated due to gravity.

2. Trajectory:
- The path followed by a projectile is typically a parabola.
- The shape of the trajectory is influenced by the initial velocity, launch angle, and height.

3. Key Parameters:
- Initial Velocity (v₀): The speed at which the projectile is launched.
- Launch Angle (θ): The angle at which the projectile is launched relative to the horizontal.
- Time of Flight (T): The total time the projectile remains in the air.
- Maximum Height (H): The highest point reached by the projectile.
- Range (R): The horizontal distance traveled by the projectile from launch to landing.

4. Equations of Motion:
- The equations of motion can be used to calculate various parameters:
- Horizontal motion: x = v_0x· t (where v_0x = v_0 ·cos(θ))
- Vertical motion: y = v_0y· t - 1/2 g t^2 (where v_0y = v_0 ·sin(θ))
- g is the acceleration due to gravity (approximately 9.81 m/s²).

5. Factors Affecting Projectile Motion:
- Initial Velocity: Higher initial velocities increase range and height.
- Launch Angle: A launch angle of 45 degrees typically gives the maximum range for a given initial velocity in a vacuum.
- Air Resistance: In real-world scenarios, air resistance can affect the trajectory, making it deviate from the ideal parabolic path.

▎Applications:
Projectile motion concepts are applied in various fields such as sports (e.g., basketball, golf), engineering (e.g.,

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