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Projectile Motion Fundamentals

Sep 7, 2025

Overview

This lecture covers the fundamentals of projectile motion, demonstrating how horizontal and vertical motions are independent and how to solve related problems by splitting vectors into components.

Understanding Projectile Motion

  • Projectile motion describes objects thrown or launched that move in both horizontal (x) and vertical (y) directions.
  • The path of a projectile is a parabola, with motion described separately in x and y directions.
  • Horizontal and vertical motions are independent; equations for each can be applied separately.

Independence of Motion

  • Two marbles, one dropped and one rolled off a surface from the same height, hit the ground at the same time.
  • Vertical motion (airtime) is independent of the object's horizontal velocity.

Components of Motion & Vector Decomposition

  • Velocity vectors can be split into x (horizontal) and y (vertical) components using trigonometry.
  • Vₓ (horizontal) = initial velocity × cos(angle); Vᾧ (vertical) = initial velocity × sin(angle).
  • In the absence of air resistance, horizontal velocity remains constant; vertical velocity changes due to gravity.

Solving Projectile Motion Problems

  • To find time in air, solve for the y-direction using displacement, initial vertical velocity, and acceleration due to gravity.
  • Use the time of flight and constant horizontal velocity to calculate range (horizontal distance traveled).
  • Example: For a rock thrown at 30° from a 100m cliff with 8.5 m/s initial velocity:
    • Vₓ = 7.36 m/s, Vᾧ = 4.25 m/s.
    • Time in air (using quadratic formula) = 4.97 s.
    • Horizontal distance = 7.36 m/s × 4.97 s = 36.6 m.

Key Terms & Definitions

  • Projectile motion — The motion of an object thrown or launched, moving under gravity in both horizontal and vertical directions.
  • Component — Portion of a vector along either the x or y axis.
  • Velocity vector — Arrow showing both speed and direction of motion.
  • Parabola — The curved path followed by a projectile.
  • Quadratic formula — Method to solve for time in the air when displacement and velocity are known.

Action Items / Next Steps

  • Practice splitting velocity vectors into x and y components using trigonometry.
  • Solve example problems calculating time of flight and range for various projectile scenarios.

Full transcript