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Projectile motion | AP Physics | Khan Academy

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Key takeaways

Science and Nature

Scientific concepts / discoveries / phenomena

Projectile motion and independence of components

  • When air resistance is neglected, horizontal and vertical motions can be analyzed separately.
  • Vertical motion is affected by gravity.
  • Horizontal motion (ideal case) has zero acceleration, so horizontal velocity remains constant.

Equal fall time for horizontal vs. dropped launch

  • A baseball launched horizontally and another dropped from the same height hit the ground at the same time.
  • Reason: their vertical velocities match at every moment, so their vertical motion is identical.

Kinematics under constant gravitational acceleration

  • Near Earth, vertical acceleration magnitude is:

    • [ g \approx 9.8\ \text{m/s}^2 ]

  • The sign of gravitational acceleration depends on the coordinate system:

    • If up is positive, then:

      • [ a_y = -9.8\ \text{m/s}^2 ]

    • If down is positive, then:

      • [ a_y = +9.8\ \text{m/s}^2 ]

  • During the fall, vertical velocity increases in magnitude due to constant downward acceleration.

Effect of launch speed (horizontal component)

  • Changing the horizontal launch speed affects the horizontal travel distance before landing (it falls closer/farther).
  • It does not change the vertical motion or the time to hit the ground.

Projectile launched at an angle

  • Resolve the initial velocity into components:
    • Horizontal component ((v_{x0})): constant horizontal velocity (since (a_x = 0)).
    • Vertical component ((v_{y0})): motion under gravity.
  • Vertical behavior resembles:
    • throwing upward then falling
  • Specifically:
    • Velocity decreases while moving up (opposite gravity),
    • becomes zero at the top (turning point),
    • then increases while falling.
  • The trajectory is a 2D plane path (even though motion may occur in 3D space), with independent horizontal and vertical dynamics.

Free fall and ideal projectile assumptions

  • Free fall means motion under gravity only.
  • Real objects are not perfectly projectile due to air resistance.
  • Rockets are not projectile motion because of thrust/other forces.
  • Under idealization (ignore air resistance), a projectile remains gravity-driven motion, even if launched with an initial upward component.

Equations of motion usage (kinematics)

  • Horizontal acceleration is zero:
    • horizontal velocity is constant
    • position/velocity follow kinematic relations with (a_x = 0)
  • Vertical acceleration is (g) (sign depends on the coordinate choice).
  • Emphasized method:
    1. Use kinematics to find horizontal position/velocity after time (t),
    2. Use kinematics to find vertical position/velocity after time (t),
    3. Combine components to get the overall trajectory.

Methodology / analysis workflow (as described)

  • Take slow-motion snapshots of both balls at regular intervals (e.g., every 0.1 s).
  • Compare their positions over time by focusing on vertical alignment:
    • show that their vertical positions (and thus vertical velocities) match at each moment.
  • Decompose projectile motion into independent components:
    • resolve velocity into horizontal and vertical parts,
    • treat vertical motion with constant acceleration (g),
    • treat horizontal motion as constant velocity (since (a_x = 0)).
  • Reconstruct the trajectory by combining horizontal and vertical results.

Researchers / sources featured

  • No specific researchers or external sources are mentioned.

Original video