Projectile Motion Lecture Notes

Introduction to Projectile Motion

• Definition: Motion of an object moving in both horizontal and vertical directions simultaneously (e.g., a cannonball fired at an angle).
• Path Representation: The trajectory of projectiles can be represented by a parabola.

Independence of Motion

• Horizontal and vertical motions are independent of each other.
  • Use separate equations for horizontal (x) and vertical (y) motions.
• Example: Two marbles dropped:
  • One dropped straight down, another rolls off a surface.
  • Both strike the ground at the same time despite differences in horizontal motion.

Example: Rock Thrown from a Cliff

• Scenario: Throwing a rock at a 30-degree angle from a 100-meter cliff with an initial velocity of 8.5 m/s.
• Questions to Answer:
  1. How long before the rock hits the ground?
  2. How far from the edge of the cliff will it land?

Analyzing the Motion

1. Time in Air: Relates only to vertical (y) direction; independent of horizontal velocity.
2. Distance Traveled: Depends on horizontal (x) velocity and time in air.

Velocity Components

• Split velocity vector into x and y components:
  • Horizontal Velocity (Vx): Remains constant.
  • Vertical Velocity (Vy): Changes due to gravity; maximum at launch, decreases to zero at zenith, and increases negatively until ground impact.
• Calculating Components:
  • Vx = 8.5 m/s * cos(30°) = 7.36 m/s
  • Vy = 8.5 m/s * sin(30°) = 4.25 m/s

Time of Flight Calculation

• Use kinematics for vertical motion:
  • Displacement (y) = -100 m (downward).
  • Initial vertical velocity (Vy) = 4.25 m/s.
  • Acceleration (a) = -9.81 m/s² (gravity).
• Solve for time (t) using quadratic equation:
  • Result: t ≈ 4.97 seconds.

Horizontal Distance Calculation

• Distance from cliff edge:
  • Distance = Vx * time = 7.36 m/s * 4.97 s ≈ 36.6 meters.

Conclusion

• Projectile motion can be analyzed as two independent one-dimensional motions by breaking down the velocity vector into its components.
• Understanding these principles simplifies calculations and predictions of projectile behavior.

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