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Projectile Motion Overview

Sep 11, 2025

Overview

This lecture introduces projectile motion, explaining how to analyze motion in two dimensions by separating variables and equations for the x and y directions.

Review of Previous Motion Concepts

  • Previous studies focused on linear motion: constant velocity, constant acceleration, and free-fall.
  • Linear motion only considers one dimension.

Introduction to Projectile Motion

  • Projectile motion involves objects moving in two dimensions (x and y) through the air with no air resistance.
  • The strategy for solving projectile motion problems is to separate variables for x and y directions.

Motion in the Y Direction (Vertical)

  • In the y direction, the object is in free-fall with acceleration of -9.81 m/sĀ² (downward, on Earth).
  • The y direction uses the UAM (Uniformly Accelerated Motion) equations.
  • Five UAM variables: initial velocity, final velocity, acceleration, displacement, and time.
  • Four UAM equations relate these variables; knowing three allows solving for the other two.

Motion in the X Direction (Horizontal)

  • In the x direction, there is no acceleration (a_x = 0).
  • The object moves at a constant velocity horizontally.
  • The equation for x direction: velocity (v_x) = displacement (Ī”x) / time (Ī”t).
  • Only two variables are needed to solve for the third in the x direction.

Solving Projectile Motion Problems

  • Always separate and list known variables for both x and y directions.
  • Usually solve for the change in time (Ī”t) first, as it is a scalar and independent of direction.
  • After finding time, use it in the other direction's equation.

Key Terms & Definitions

  • Projectile Motion ā€” Motion of an object in two dimensions under only gravity, no air resistance.
  • Free-fall ā€” Motion under gravity alone, with acceleration of -9.81 m/sĀ².
  • UAM Equations ā€” Equations for uniformly accelerated motion.
  • Scalar ā€” Quantity with magnitude only; time is a scalar.
  • Constant Velocity ā€” Motion at unchanging speed and direction (in the x direction for projectiles).

Action Items / Next Steps

  • Practice separating x and y variables and equations in example projectile motion problems.
  • Review and memorize the UAM equations.
  • Prepare for solving problems where you must find time and use it in both directions.

Full transcript