Overview
This lecture explained the horizontal and vertical motions of a projectile, reviewed Newton’s second law, and demonstrated how to solve problems involving horizontally launched projectiles.
Review of Newton’s Second Law and Acceleration
- Newton’s second law: Net force on an object equals its mass times acceleration (F = ma).
- Acceleration is the rate at which velocity changes with time; it has both magnitude and direction (vector quantity).
- Most everyday motion is not at constant acceleration due to changing forces.
- Uniformly accelerated motion (UAM) occurs when acceleration remains constant over time.
Uniformly Accelerated Motion (UAM)
- UAM means velocity changes by the same amount in each equal time interval.
- Examples of UAM: objects in free fall, rocks falling, a vehicle speeding up steadily.
- Acceleration due to gravity (g) on Earth is 9.8 m/s², directed downward.
Vertical and Horizontal Motion
- Gravity causes objects to fall towards Earth, pulling them down when thrown upward.
- Free-falling objects or objects dropped exhibit UAM due to constant g.
- In UAM, acceleration is constant; in uniform motion, acceleration is zero.
Projectile Motion and Its Components
- Projectile motion occurs when an object moves in a curved (parabolic) path under gravity.
- The path followed by a projectile is called its trajectory.
- Projectile motion has two independent components: horizontal (x-axis) and vertical (y-axis).
- Horizontal component:
- No resistance, constant velocity (vx), zero acceleration (ax).
- The horizontal distance is called range (dx).
- Vertical component:
- Affected by gravity (ay = g = -9.8 m/s²), velocity (vy) changes, acceleration is constant and downward.
- Vertical distance is height (h or dy).
Example Problem: Horizontally Launched Projectile
- Given: Initial horizontal velocity (vi = 1.50 m/s), range (dx = 0.70 m), g = 9.8 m/s².
- Time to fall: t = dx/vi = 0.47 s.
- Height of table: dy = ½ g t² = 1.08 m.
- Final vertical velocity: vfy = √(2g dy) = -4.6 m/s (downward).
- Final speed before hitting cup: vr = √(vfx² + vfy²) = 4.84 m/s.
Key Terms & Definitions
- Uniformly Accelerated Motion (UAM) — Motion with constant acceleration.
- Projectile — An object thrown or projected, subject only to gravity.
- Trajectory — The curved path followed by a projectile.
- Range (dx) — The horizontal distance traveled by a projectile.
- Height (h or dy) — The vertical distance fallen by a projectile.
- Resultant velocity (vr) — Combined speed from both horizontal and vertical components.
Action Items / Next Steps
- Review formulas for projectile motion, especially how to solve for time, height, and velocity components.
- Watch part 2 of the lesson for more examples and practice.
- Practice solving horizontally launched projectile problems.