Projectile Motion

Jul 3, 2024

Projectile Motion

Introduction

  • Understanding the concept of projectile motion.
  • Initial velocity and its role in projectile motion.
  • The effects of gravity and resistance on motion.

Key Concepts

Initial Velocity

  • The initial velocity of a projectile is maximum when it is thrown.
  • Initial velocity decreases over time due to gravity and air resistance.

Gravity

  • Gravity is the only force acting on a projectile in ideal scenarios (no air resistance).
  • Gravity causes the projectile to fall downward, decreasing its upward velocity and increasing its downward velocity over time.
  • Vertical velocity eventually becomes zero at the peak of the projectile's trajectory.

Motion Analysis

Upward Motion

  • Velocity decreases with time as the projectile rises.
  • At maximum height, vertical velocity is zero.

Downward Motion

  • Projectile falls back to the ground under the influence of gravity.
  • Velocity increases as the projectile descends.
  • Horizontal motion remains constant throughout.

Equations and Formulas

Horizontal Motion

  • Horizontal velocity (Ux): Ux = U * cos(θ)
  • Horizontal velocity remains constant.

Vertical Motion

  • Vertical velocity (Uy): Uy = U * sin(θ) - g * t
  • Acceleration due to gravity (g): Typically 9.8 m/s², acting downwards.
  • Vertical velocity decreases to zero at maximum height and then increases in downward direction.

Trajectory and Path

  • Projectile follows a parabolic path.
  • Maximum height (H): Point where vertical velocity is zero.
  • Range: The horizontal distance covered by the projectile.
  • Time of flight: Total time the projectile remains in the air.

Examples and Applications

Practical Scenarios

  • Understanding projectile motion can help in sports, such as basketball or football.
  • Engineers use projectile motion concepts in designing various components and structures.

Summary

  • Projectile motion involves both vertical and horizontal components of motion.
  • Gravity affects vertical motion while horizontal motion remains constant barring air resistance.
  • Understanding the initial velocity, gravity, and resistance helps in determining the path and behavior of a projectile.