Overview
This lecture explains projectile motion, focusing on how to analyze an object's motion in both horizontal and vertical directions using kinematic equations and vector components.
Introduction to Projectile Motion
- Projectile motion refers to objects thrown or launched that move in both horizontal (x) and vertical (y) directions.
- The path of a projectile is a parabola.
- Horizontal and vertical motions are independent of each other.
Independence of Motion
- Horizontal motion does not affect vertical motion and vice versa.
- Two marbles dropped and projected horizontally from the same height hit the ground simultaneously.
- Air time for projectiles depends only on vertical motion.
Components of Motion
- The horizontal (x-axis) distance depends on horizontal velocity and air time.
- The vertical (y-axis) motion determines how long the projectile stays in the air.
- Velocity at any moment can be split into horizontal ((v_x)) and vertical ((v_y)) components.
- Horizontal velocity remains constant if air resistance is ignored.
- Vertical velocity changes due to gravity.
Solving Projectile Problems
- Split the initial velocity vector into (x) and (y) components using trigonometry:
- (v_x = v \cos \theta)
- (v_y = v \sin \theta)
- Example: For a 30° launch angle and 8.5 m/s velocity:
- (v_x = 8.5 \cos 30^\circ = 7.36) m/s
- (v_y = 8.5 \sin 30^\circ = 4.25) m/s
- To find air time, use only the vertical component in kinematic equations.
- Use displacement, initial vertical velocity, and gravity to solve for time.
- Use air time and horizontal velocity to calculate range.
Example Calculation
- Throwing a rock at 30° from a 100 m cliff with 8.5 m/s velocity:
- Air time: 4.97 seconds (using vertical motion).
- Range: (7.36 \text{ m/s} \times 4.97 \text{ s} = 36.6) meters from the cliff.
Key Terms & Definitions
- Projectile Motion — Motion of an object thrown or launched, moving in both x and y directions under gravity.
- Vector Components — Breaking a velocity vector into horizontal ((v_x)) and vertical ((v_y)) parts.
- Kinematic Equations — Formulas describing motion with constant acceleration.
- Range — Horizontal distance a projectile travels.
Action Items / Next Steps
- Practice splitting velocity into x and y components for various angles.
- Solve sample projectile motion problems using kinematic equations.