Motion, Mechanics & Gravity
Rigorous physics calculations for planetary gravitational free fall, vehicular braking distances across surface friction coefficients, and 2D parabolic projectile trajectories.
Free Fall Time
Earth, Moon, Mars & JupiterBraking Distance
Speed, Friction & ReactionProjectile Motion
2D Trajectory & Range PlotterFree Fall Drop Time & Impact Velocity
Classical Newtonian Kinematics in Vacuum (NIST Reference CODATA)
Elapsed duration for an object to reach ground in vacuum from 10 m.
Drop Time Comparison Across Solar System (10.0m Drop)
t ∝ 1/√gskymotion20-20).Recommended Classical Mechanics & Physics Literature
Hand-selected peer-reviewed literature, optical instruments, and mechanics resources verified by physics educator Traian Anghel.
The Feynman Lectures on Physics, Vol. 1
By Richard Feynman, Robert Leighton & Matthew Sands. Mechanics, radiation, kinetics, and heat.
Classical Mechanics by John R. Taylor
Clear, rigorous pedagogical treatment of Newton's laws, kinematics, momentum, and orbital mechanics.
Physics for Scientists and Engineers
By Raymond A. Serway & John W. Jewett. Comprehensive kinetic energy, work, and friction mechanics.
What the free-fall calculator predicts
The solver calculates the time and final speed of an object released from rest through a selected vertical height under a constant planetary gravitational acceleration. It is a reference model for ideal gravitational motion.
Method & formula
Starting from h = ½gt², the fall time is t = √(2h/g). Final speed is v = gt = √(2gh). The object’s mass cancels, so all bodies share the same acceleration under the model’s assumptions.
Inputs
Enter the drop height and choose the celestial body. The selected planet changes g; unit controls convert the height for display while the calculation uses SI meters and seconds.
How to read the result
Time is the interval from release to the selected lower level. Impact velocity is the ideal downward speed immediately before arrival. Comparing planets demonstrates how surface gravity changes both duration and velocity.
Assumptions & limits
The calculation assumes vacuum, release from rest, constant g, no buoyancy, no wind, and a flat vertical displacement. Real objects experience drag and may rotate; large falls also require changing air density and gravitational field strength.
Reference: Classical constant-acceleration kinematics using standard gravitational values.
Automotive Braking & Total Stopping Distance
AASHTO Geometric Highway Design & Newtonian Friction Model
Distance traveled during 1.5s before pressing the brake pedal.
Tire friction work required to dissipate kinetic energy (v² / (2μg)).
Reaction distance, braking distance, and total stopping distance
The calculator separates the distance traveled before the driver applies the brakes from the physical distance required to dissipate the vehicle’s kinetic energy after braking begins.
Method & formula
Total distance is d = vtᵣ + v²/(2μg). The first term grows linearly with speed and reaction time; the braking term grows with speed squared and decreases as the tire–road friction coefficient μ increases.
Inputs
Set vehicle speed, choose a representative road surface, and adjust reaction time. Speed is converted to meters per second; the surface preset supplies an approximate friction coefficient.
How to read the result
Reaction and braking results should be added, not compared as alternatives. Doubling speed doubles reaction distance but approximately quadruples ideal braking distance, which explains the rapidly increasing total at highway speeds.
Assumptions & limits
This is an ideal level-road estimate, not a safe following-distance prescription. Tire condition, ABS behavior, vehicle loading, brake temperature, road gradient, standing water, ice, visibility, and driver condition can materially change real stopping distance.
Reference: Work–energy mechanics and representative AASHTO-style friction calculations.
Projectile Motion & Parabolic Trajectory
Classical 2D Kinematics in Vacuum (Halliday & Resnick)
Total horizontal distance traveled until impact.
Peak vertical altitude at trajectory apex.
Total airborne duration from launch to ground.
How the projectile trajectory is calculated
The trajectory solver resolves launch velocity into horizontal and vertical components, then calculates range, maximum height, total flight time, and a plotted parabolic path under uniform gravity.
Method & formula
For launch and landing at equal height, range is R = v₀²sin(2θ)/g, apex height is H = v₀²sin²(θ)/(2g), and flight time is T = 2v₀sin(θ)/g.
Inputs
Choose initial speed, launch angle, and gravitational acceleration. The graph samples the horizontal and vertical position equations from launch until the projectile returns to its starting elevation.
How to read the result
At equal launch and landing height in vacuum, 45° maximizes range. Complementary angles such as 30° and 60° produce the same range but different apex heights and flight durations.
Assumptions & limits
The model excludes aerodynamic drag, lift, spin, wind, object size, Earth curvature, and unequal launch and landing elevations. A real ball, arrow, or golf shot can differ substantially, especially at high speed or long range.
Reference: Standard two-dimensional Newtonian kinematics for a projectile in a uniform gravitational field.
skymotion20-20).Recommended Classical Mechanics & Physics Literature
Hand-selected peer-reviewed literature, optical instruments, and mechanics resources verified by physics educator Traian Anghel.
The Feynman Lectures on Physics, Vol. 1
By Richard Feynman, Robert Leighton & Matthew Sands. Mechanics, radiation, kinetics, and heat.
Classical Mechanics by John R. Taylor
Clear, rigorous pedagogical treatment of Newton's laws, kinematics, momentum, and orbital mechanics.
Physics for Scientists and Engineers
By Raymond A. Serway & John W. Jewett. Comprehensive kinetic energy, work, and friction mechanics.
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