Comprehensive Notes on 2D Projectile Motion

Chapter 3: Motion in a Plane (2D Motion)

Overview

• Goal: To integrate two-dimensional (2D) vectors with kinematic formulas.

• Vocabulary:

  • Projectile Motion: A key concept for understanding 2D motion under gravity.

• Quantities, Variables, SI Units: No new quantities, variables, or SI units are introduced; previous kinematic understanding applies.

Projectile Motion Basics

• Definition: Projectile motion is characterized as free-fall while simultaneously moving horizontally.

• Key Acceleration: Due to gravity, the acceleration in the vertical (y) direction is constant:

  • $a_y = -g$ (where $g hickapprox 9.8 \; m/s^2$, assuming the positive y-direction is upwards).

• Assumption: Air resistance is ignored in these calculations.

Independence of x and y Motion

• Fundamental Principle: Motion in the x-direction has absolutely no effect on motion in the y-direction, and vice-versa.

• x-direction:

  • Experiences no acceleration (assuming no air resistance or other horizontal forces), meaning $a_x = 0$.

  • Thus, horizontal velocity ( $v_x$ ) remains constant throughout the flight.

• y-direction:

  • Experiences acceleration due to gravity, $a_y = -g$.

  • The vertical velocity ( $v_y$ ) changes linearly with time.

• Overall Motion: Projectile motion is a combination of these independent motions in both the x and y directions.

Illustrative Example: Car and Ball (Page 4)

• Scenario: While driving at a constant speed, a ball is thrown straight upward through an open sunroof.

• Question: Where does the ball land (ignoring air resistance, wind)?

• Analysis: Because the ball shares the car's constant horizontal velocity and horizontal motion is independent of vertical motion, the ball maintains the same horizontal position relative to the car while it goes up and comes back down.

• Answer: B. In the car.

• Related Concept: Demonstrated by a