Overview
This lecture introduces projectile motion, distinguishes one-dimensional and two-dimensional cases, reviews relevant kinematic equations, and highlights key problem-solving strategies.
Introduction to Projectile Motion
- Projectile motion describes objects moving through air under only the influence of gravity.
- The object's initial speed and angle determine its path, called the trajectory.
- Air resistance is ignored for calculation simplicity.
- Vertical acceleration is always 9.8 m/sĀ² downward (denoted as "g"), while horizontal acceleration is zero.
Definitions and Key Concepts
- Projectile: An object in projectile motion.
- Trajectory: The path followed by a projectile.
- Projectile motion only applies while the object is airborne and not touching anything else.
- The horizontal velocity (vx) remains constant; vertical velocity (vy) changes due to gravity.
1D vs 2D Projectile Motion
- One-dimensional (1D): Projectile moves only vertically (up or down); only y-direction equations used.
- Two-dimensional (2D): Projectile moves both horizontally and vertically; requires x and y kinematic equations.
- In this course, all such cases are called projectile motion, further split into 1D and 2D.
Applying Kinematic Equations
- For 1D, use y-direction equations with acceleration a = -g.
- For 2D, use both x (a = 0, velocity constant) and y (a = -g) equations.
- In 2D, initial velocity is often given as magnitude and angle, requiring calculation of x and y components.
Key Problem-Solving Points
- Important trajectory points: initial, maximum height (vy = 0), and final.
- Symmetric trajectories occur if the initial and final heights are equal; time to max height is half total time.
- The range is the horizontal distance between start and end points.
- Time of flight depends only on vertical motion.
- Vertical velocity has equal magnitude and opposite direction at the same height before and after the peak (if starting/ending heights match).
- Treat x and y motions independently for calculations.
Key Terms & Definitions
- Projectile ā an object moving through air influenced only by gravity.
- Trajectory ā the path of a projectile.
- Range ā the horizontal distance traveled by a projectile.
- Freefall ā motion under gravity alone, sometimes used interchangeably with projectile motion.
Action Items / Next Steps
- Review and organize x and y kinematic equations for both 1D and 2D projectile motion.
- Prepare for detailed examples and problem-solving in the next lesson.