Free Fall & Gravity Drop

Compute time to fall and impact velocity from a given height. Toggle air resistance and switch between Earth, Moon, and Mars. Includes live animation plus y(t) and v(t) graphs.

Inputs
Results
Time to impact
Impact speed
Terminal speed (est.)
Animation
Ball falls from height h to ground (y=0). With air resistance on, motion approaches terminal speed.
t = 0.00 s
Graphs
Comparisons
Color Label h g v0 timpact vimpact
Formula Breakdown
No Air Resistance
  • Time to impact: t = (-v₀ + √(v₀² + 2 g h)) / g
  • Impact speed: v = v₀ + g · t
  • Height profile: y(t) = h − v₀ t − ½ g t²
With Quadratic Drag
  • Simulated from m dv/dt = m g − ½ ρ Cd A v |v|
  • Position from dy/dt = v integrated numerically (time step 0.005 s)
  • Terminal speed estimate: vt = √(2 m g / (ρ Cd A))
FAQ & Teaching Notes
Concept Focus

Highlight that in a vacuum, all objects share the same acceleration g regardless of mass.

  • Use the presets to compare Earth, Moon, and Mars.
  • Toggle air drag to contrast analytic vs. numeric motion.
Classroom Moves

Freeze the animation at quarter intervals and ask students to match the position with points on y(t).

  • Invite students to predict impact speed before revealing calculations.
  • Assign planet overlays to different lab groups for mini-presentations.
Misconception Alert

“Heavier falls faster” only holds with drag. Show how terminal speed depends on mass, area, and drag coefficient.

  • Adjust mass while drag is on to see vt change.
  • Discuss why skydivers change body posture to alter drag.
What assumptions are used?
Constant gravity and either no drag (analytic), or quadratic drag with constant air density for the numerical simulation.
How can I connect to energy ideas?
Ask students to compute potential energy (mgh) at release and kinetic energy (½mv²) at impact, then compare with and without drag to explain where the “missing energy” goes.
What is terminal velocity?
The speed where drag balances weight: vt = √(2 m g / (ρ Cd A)). For lighter or larger objects, vt is lower.

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About This Tool & Methodology

Computes free‑fall distance, time, and velocity under uniform gravity (optionally with initial velocity). Uses SI units and the standard kinematics equations.

Learning Outcomes

  • Relate position, velocity, and acceleration due to gravity.
  • Explore initial velocity effects and time symmetry.
  • Practice unit consistency and typical g values.

Authorship

  • Author: Anish Nath — Follow on X
  • Last updated: 2025-11-19

Trust & Privacy

  • Runs locally in your browser.