Overview
This lecture covers the fundamentals of projectile motion, emphasizing the independence of horizontal and vertical motion, how to analyze projectiles by splitting velocity into components, and solving related problems using kinematic equations.
Projectile Motion Basics
- Projectile motion involves an object moving both horizontally and vertically after being launched.
- The path of a projectile is a parabola due to simultaneous constant horizontal velocity and vertical acceleration from gravity.
- Horizontal (x) and vertical (y) motions are independent; each can be analyzed with separate kinematic equations.
Independence of Motion
- Horizontal velocity does not affect how long a projectile is in the air; airtime is determined solely by vertical motion.
- Two objects dropped from the same height (one with horizontal velocity and one without) will hit the ground simultaneously.
Components of Velocity
- Any initial velocity at an angle can be split into horizontal (Vx) and vertical (Vy) components.
- Use trigonometry: Vx = V * cos(Īø), Vy = V * sin(Īø).
- In the example, V = 8.5 m/s at 30Ā° gives Vx = 7.36 m/s and Vy = 4.25 m/s.
Analyzing Projectile Problems
- To find airtime, use vertical motion formulas with the y-component of velocity.
- Displacement, initial vertical velocity, and gravity are used to solve for time in the air.
- Use the horizontal component and total airtime to calculate how far from the edge the projectile lands.
- Horizontal velocity remains constant (ignoring air resistance); vertical velocity changes due to gravity.
Example Problem Recap
- Rock thrown off a 100 m cliff at 8.5 m/s, 30Ā° above horizontal.
- Time in the air: 4.97 s (solved using vertical motion).
- Horizontal distance traveled: 36.6 m (Vx Ć time).
Key Terms & Definitions
- Projectile motion ā Motion of an object thrown or launched, moving in both x and y directions under gravity.
- Component ā Part of a vector in either horizontal (x) or vertical (y) direction.
- Kinematic equations ā Formulas describing motion with constant acceleration.
- Initial velocity (Vā) ā Speed and direction at which an object is launched.
Action Items / Next Steps
- Practice splitting velocity vectors into x and y components.
- Solve more projectile motion problems using separate x and y analyses.
- Review kinematic equations for both directions.