MECHANICSKinematicsPhysics Calculator
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Free Fall

Free fall is motion under gravity only (neglecting air resistance). Equations: t = โˆš(2h/g), v = โˆš(2gh), h = ยฝgtยฒ. All objects fall at the same rate regardless of mass โ€” Galileo's key insight. Supports Earth, Moon, Mars, and other planetary gravities.

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Earth g โ‰ˆ 9.81 m/sยฒ; Moon 1.62 m/sยฒ; Mars 3.71 m/sยฒ; Jupiter 24.79 m/sยฒ. Time to fall 100 m on Earth: t = โˆš(200/9.81) โ‰ˆ 4.5 s; v โ‰ˆ 44 m/s at impact. Thrown upward: max height h_max = hโ‚€ + vโ‚€ยฒ/(2g); time up = time down. Terminal velocity: when drag = weight; ~55 m/s for skydiver, ~9 m/s for raindrop.

Key quantities
t = โˆš(2h/g)
Time to Fall
Key relation
v = โˆš(2gh)
Impact Velocity
Key relation
h = ยฝgtยฒ
Height Fallen
Key relation
PE + KE = constant
Energy
Key relation

Ready to run the numbers?

Why: Free fall governs skydiving, dropped objects, and orbital mechanics. Understanding g, impact velocity, and drop time is essential for safety and engineering.

How: With zero initial velocity, distance h = ยฝgtยฒ and final velocity v = gt = โˆš(2gh). Energy is conserved: PE lost = KE gained. Air resistance becomes significant at high speeds (terminal velocity).

Earth g โ‰ˆ 9.81 m/sยฒ; Moon 1.62 m/sยฒ; Mars 3.71 m/sยฒ; Jupiter 24.79 m/sยฒ.Time to fall 100 m on Earth: t = โˆš(200/9.81) โ‰ˆ 4.5 s; v โ‰ˆ 44 m/s at impact.

Run the calculator when you are ready.

Calculate Free FallEnter height, time, or velocity to find missing parameters

๐Ÿ“š Famous Free Fall Scenarios

Explore classic physics experiments and real-world free fall examples:

For educational and informational purposes only. Verify with a qualified professional.

๐Ÿ”ฌ Physics Facts

๐ŸŽ

Galileo showed all objects fall at the same rate (ignoring air) โ€” contradicting Aristotle's belief that heavier objects fall faster.

โ€” Galileo Galilei (1638)

๐ŸŒ

Earth g varies: 9.78 m/sยฒ at equator, 9.83 m/sยฒ at poles due to rotation and oblateness.

โ€” NIST

๐Ÿช‚

Terminal velocity for skydiver: ~55 m/s (120 mph); for penny ~9 m/s (not lethal).

โ€” Physics of skydiving

๐ŸŒ™

On the Moon, Apollo 15 astronaut dropped hammer and feather โ€” they hit the ground simultaneously.

โ€” NASA Apollo 15

โš™๏ธ Free Fall Parameters

What do you want to calculate?

Motion Parameters

Height above ground (in meters)
Positive = up, Negative = down
Time of fall (seconds)
Mass of falling object

Gravitational Environment

Gravitational acceleration
free-fall@bloomberg:~$
VELOCITY: HIGH

๐Ÿ“Š Free Fall Analysis Results

Time of Fall
4.52
seconds
Impact Velocity
44.29
m/s (159.5 km/h)
Distance Fallen
100.00
meters
Max Height
100.00
meters
Initial PE
981.00 J
Final KE
981.00 J
Average Velocity
22.15 m/s
Energy Status
Conserved โœ“

๐Ÿ“ˆ Free Fall Analysis Dashboard

๐Ÿ“ Height vs Time

Position during free fall

๐Ÿš€ Velocity vs Time

Speed increasing during fall

๐Ÿช Planetary Comparison

Fall time on different celestial bodies

โšก Energy Conservation

PE โ†’ KE energy transformation

๐Ÿ“ Step-by-Step Solution

๐Ÿ“Š Input Parameters

Calculation Mode: FIND TIME

Initial Height: 100.00 m

Initial Velocity: 0.00 m/s (upward)

Gravitational Acceleration: 9.81 m/sยฒ (Earth)

๐Ÿงฎ Free Fall Calculations

Time to fall (dropped from rest): t = โˆš(2h/g)

t = โˆš(2 ร— 100.00 / 9.81)

โ†’ t = 4.5152 seconds

โšก Energy Analysis

Initial Potential Energy: PE = mgh

PE = 1.00 ร— 9.81 ร— 100.00

โ†’ PE = 981.0000 J

Kinetic Energy at Impact: KE = ยฝmvยฒ

KE = 0.5 ร— 1.00 ร— 44.2945ยฒ

โ†’ KE = 981.0000 J

Energy Conservation: PE_initial + KE_initial = KE_final

โ†’ 981.0000 J โ‰ˆ 981.0000 J

๐Ÿ—๏ธ Famous Heights Reference

LandmarkHeight (m)Fall TimeImpact Velocity
๐ŸŽNewton's Apple Tree30.78 s7.7 m/s (28 km/h)
๐ŸŠHigh Dive Platform101.43 s14.0 m/s (50 km/h)
๐Ÿ๏ธCliff Diving (World)272.35 s23.0 m/s (83 km/h)
๐Ÿ›๏ธLeaning Tower of Pisa573.41 s33.4 m/s (120 km/h)
๐Ÿ’งNiagara Falls513.22 s31.6 m/s (114 km/h)
๐Ÿ—ฝStatue of Liberty934.35 s42.7 m/s (154 km/h)
๐Ÿ•ฐ๏ธBig Ben964.42 s43.4 m/s (156 km/h)
๐Ÿช‚Base Jump Legal Min1505.53 s54.2 m/s (195 km/h)

๐Ÿ“– What is Free Fall?

Free fall is the motion of an object under the sole influence of gravity, with no other forces (like air resistance) acting on it. This idealized motion was first studied systematically by Galileo Galilei in the late 16th century.

๐ŸŽ Key Principles

  • โ€ข All objects fall at the same rate (ignoring air resistance)
  • โ€ข Acceleration is constant: g = 9.81 m/sยฒ on Earth
  • โ€ข Velocity increases linearly with time
  • โ€ข Distance increases with the square of time

๐ŸŒ Galileo's Discovery

  • โ€ข Disproved Aristotle's claim about mass affecting fall rate
  • โ€ข Demonstrated with balls of different masses
  • โ€ข Led to Newton's laws of motion
  • โ€ข Foundation of modern physics

In reality, air resistance affects falling objects, especially at high speeds. However, free fall equations provide an excellent approximation for dense objects over short distances.

๐Ÿงฎ Free Fall Equations

Time to Fall

t = โˆš(2h/g)

Example: Object dropped from 100m on Earth
t = โˆš(2 ร— 100 / 9.81) = 4.52 seconds

Impact Velocity

v = โˆš(2gh)

Example: Same 100m drop
v = โˆš(2 ร— 9.81 ร— 100) = 44.3 m/s

Complete Free Fall Equations

Height fallen:

h = ยฝgtยฒ

Velocity at time t:

v = gt

Thrown upward max height:

h_max = vโ‚€ยฒ/(2g)

Total air time (thrown up):

t_total = 2vโ‚€/g

โฐ When to Use This Calculator

๐ŸŽ“ Education

  • โ€ข Physics homework and labs
  • โ€ข Understanding gravity concepts
  • โ€ข Comparing planetary physics
  • โ€ข Energy conservation demonstrations

โš™๏ธ Engineering

  • โ€ข Drop testing calculations
  • โ€ข Impact force estimation
  • โ€ข Safety engineering
  • โ€ข Aerospace applications

๐ŸŽฌ Entertainment

  • โ€ข Stunt calculations
  • โ€ข Skydiving planning
  • โ€ข Bungee jump design
  • โ€ข Special effects physics

๐Ÿช Gravity Across the Solar System

BodyGravity (m/sยฒ)% of EarthFun Fact
๐ŸŒEarth9.81100%
๐ŸŒ™Moon1.6217%You could jump 6x higher!
๐Ÿ”ดMars3.7138%Similar to 3 floors up on Earth
๐ŸŸ Jupiter24.79253%You'd weigh 2.5x more
๐ŸŸกVenus8.8790%
โšชMercury3.7038%
๐ŸชSaturn10.44106%
๐Ÿ”ตUranus8.6989%
๐Ÿ’™Neptune11.15114%
โšซPluto0.626%

โ“ Frequently Asked Questions

What does "EXTREME", "HIGH", and "MODERATE" mean in the Bloomberg Terminal risk indicator?

The Bloomberg Terminal risk indicator categorizes impact velocity levels: "EXTREME" (v > 60 m/s) indicates velocities exceeding typical terminal velocity for humans, representing life-threatening impacts requiring immediate safety measures. "HIGH" (20-60 m/s) represents dangerous velocities requiring protective equipment and careful planning. "MODERATE" (<20 m/s) indicates manageable velocities for most controlled free fall scenarios.

How does air resistance affect free fall calculations?

This calculator uses ideal free fall equations that ignore air resistance. In reality, air resistance becomes significant at higher velocities, reducing acceleration and limiting terminal velocity. For dense objects over short distances, the ideal equations provide excellent approximations. For light objects or long falls, consider using a terminal velocity calculator.

Why do all objects fall at the same rate?

Galileo's discovery that all objects fall at the same rate (ignoring air resistance) follows from Newton's second law: F = ma. Heavier objects have more gravitational force (F = mg) but also more mass, so acceleration (a = F/m = g) is constant. This principle holds true regardless of mass when air resistance is negligible.

How does gravity differ on other planets?

Gravitational acceleration varies with planetary mass and radius: g = GM/rยฒ. On the Moon (g = 1.62 m/sยฒ), objects fall slower and take longer to reach the ground. On Jupiter (g = 24.79 m/sยฒ), objects accelerate much faster. The calculator supports all major celestial bodies and custom gravity values.

What happens when an object is thrown upward?

When thrown upward with initial velocity vโ‚€, the object decelerates due to gravity, reaches maximum height (h_max = hโ‚€ + vโ‚€ยฒ/(2g)), then falls back down. Total time in air is t_total = 2vโ‚€/g if starting from ground level. The calculator handles all upward, downward, and dropped scenarios.

How is energy conserved in free fall?

In ideal free fall, mechanical energy is conserved: PE + KE = constant. As an object falls, potential energy (PE = mgh) decreases while kinetic energy (KE = ยฝmvยฒ) increases. At impact, all initial potential energy converts to kinetic energy, satisfying energy conservation.

Can I use this calculator for projectile motion?

This calculator handles vertical motion only. For objects launched at angles (projectile motion), use a projectile motion calculator that accounts for both horizontal and vertical components. However, the vertical component follows the same free fall equations used here.

โš ๏ธ Disclaimer

Disclaimer: This calculator uses ideal free fall equations that ignore air resistance, wind effects, and other real-world factors. Results assume uniform gravitational acceleration and no external forces. Actual fall times and velocities may differ due to air resistance, especially at high speeds. For safety-critical applications (skydiving, engineering, construction), always consult professional resources, perform experimental verification, and account for air resistance, terminal velocity, and safety margins. This calculator is for educational and preliminary analysis purposes only.

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