Lecture on Projectile Motion

Key Question

• Two stones: one dropped vertically, one thrown horizontally
• Which lands last?
• Intuition might say the thrown stone lands last; that's incorrect.
• Both stones land at the same time.

Fundamental Concepts of Projectile Motion

• Projectile motion has a parabolic path.
• Caused by the effect of gravity on two velocity components:
  • Horizontal and Vertical

Velocity Components

• Horizontal Velocity
  • Unaffected by gravity
  • Stays constant throughout motion
• Vertical Velocity
  • Affected by gravity
  • Changes over time:
    1. Decreases as the object moves up
    2. Becomes zero at maximum height
    3. Increases (negatively) as the object falls down

Motion Analysis

• Horizontal and vertical distance over small time intervals creates a curved path.
• **Gravitational Force: **
  • Always acts vertically
  • Only affects vertical component
• **Trajectory Shape: **
  • Resultant path is a parabola

Thought Experiment

• Vertical ejection: ball returns to its initial position
• Cannon angle experiments:
  • Eject at various angles with same speed
  • Maximum range at 45° angle
    • Range is the product of horizontal velocity and time in air

Practical Application

• Reducing cannon angle increases horizontal velocity but decreases time in air
• Max range occurs at balanced components: 45° angle

Resolving the Initial Question

• Stone thrown horizontally vs. vertically dropped
• Vertical velocity component: Both start with zero
• Effect of Gravity: Same on both stones
• Conclusion: Both stones hit the ground at the same time