Notes on Projectile Motion

Learning Objectives

  • Define Projectile Motion

  • Explain Projectile Motion

  • Identify and differentiate the types of Projectile Motion

  • Explain kinematics equations relevant to Projectile Motion

  • Solve Projectile Motion problems

Definition of Projectile

  • Projectile: Any object projected by some means that continues to move due to its own inertia (mass).

Motion Characteristics

  • Two Dimensions: Projectiles move in two dimensions, resulting in two components similar to a resultant vector.

Velocity Components

  • Horizontal Velocity:

    • Constant, does not change

    • Covers equal displacements in equal time intervals

    • Gravity does not affect horizontal motion.

  • Vertical Velocity:

    • Changes due to gravity

    • Magnitude decreases on ascent and increases on descent

    • Direction: UPWARD on ascent, DOWNWARD on descent.

Combining Components

  • Horizontal: Constant magnitude and direction.

  • Vertical: Changing magnitude and direction.

  • Creates a parabolic trajectory.

Horizontally Launched Projectiles

  • Characteristics:

    • No upward trajectory, no initial vertical velocity

    • Initial vertical velocity = 0 m/s.

  • Equations:

    • Horizontal: x = vt

    • Vertical: y = \frac{1}{2} g t^2

  • Example: Projectile from a plane

    • Time of fall calculated with: -500 = \frac{1}{2}(-9.8)t^2

Vertically Launched Projectiles

  • Characteristics:

    • No vertical velocity at the peak

    • Vertical velocity decreases on ascent and increases on descent.

  • Separate components used in calculations:

    • Horizontal component: V_{ox} = V \cos \theta

    • Vertical component: V_{oy} = V \sin \theta

Key Equations for Projectile Motion

Practice Example

  • A place kicker kicks a football with a velocity of 20.0 m/s at an angle of 53 degrees:

    • Time in air, distance traveled, and maximum height calculated using component breakdown and kinematic equations.

Evaluation Samples

  1. Calculate hang time and distance for a football kick.

  2. Determine height of a ramp from which a skier launches.

Quote

  • "Project, launch yourself and be discovered…"