Free Fall
Free fall is motion under gravity only (neglecting air resistance). Equations: t = โ(2h/g), v = โ(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 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 = โ(200/9.81) โ 4.5 s; v โ 44 m/s at impact. Thrown upward: max height h_max = hโ + vโยฒ/(2g); time up = time down. Terminal velocity: when drag = weight; ~55 m/s for skydiver, ~9 m/s for raindrop.
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 = โ(2gh). Energy is conserved: PE lost = KE gained. Air resistance becomes significant at high speeds (terminal velocity).
Run the calculator when you are ready.
๐ 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.
๐ฌ Physics Facts
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)
Earth g varies: 9.78 m/sยฒ at equator, 9.83 m/sยฒ at poles due to rotation and oblateness.
โ NIST
Terminal velocity for skydiver: ~55 m/s (120 mph); for penny ~9 m/s (not lethal).
โ Physics of skydiving
On the Moon, Apollo 15 astronaut dropped hammer and feather โ they hit the ground simultaneously.
โ NASA Apollo 15
โ๏ธ Free Fall Parameters
What do you want to calculate?
Motion Parameters
Gravitational Environment
๐ Free Fall Analysis Results
๐ Free Fall Analysis Dashboard
๐ Height vs Time
Position during free fall
๐ Velocity vs Time
Speed increasing during fall
๐ช Planetary Comparison
Fall time on different celestial bodies
โก Energy Conservation
PE โ KE energy transformation
๐ Step-by-Step Solution
Calculation Mode: FIND TIME
Initial Height: 100.00 m
Initial Velocity: 0.00 m/s (upward)
Gravitational Acceleration: 9.81 m/sยฒ (Earth)
Time to fall (dropped from rest): t = โ(2h/g)
t = โ(2 ร 100.00 / 9.81)
โ t = 4.5152 seconds
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 981.0000 J
๐๏ธ Famous Heights Reference
| Landmark | Height (m) | Fall Time | Impact Velocity |
|---|---|---|---|
| ๐Newton's Apple Tree | 3 | 0.78 s | 7.7 m/s (28 km/h) |
| ๐High Dive Platform | 10 | 1.43 s | 14.0 m/s (50 km/h) |
| ๐๏ธCliff Diving (World) | 27 | 2.35 s | 23.0 m/s (83 km/h) |
| ๐๏ธLeaning Tower of Pisa | 57 | 3.41 s | 33.4 m/s (120 km/h) |
| ๐งNiagara Falls | 51 | 3.22 s | 31.6 m/s (114 km/h) |
| ๐ฝStatue of Liberty | 93 | 4.35 s | 42.7 m/s (154 km/h) |
| ๐ฐ๏ธBig Ben | 96 | 4.42 s | 43.4 m/s (156 km/h) |
| ๐ชBase Jump Legal Min | 150 | 5.53 s | 54.2 m/s (195 km/h) |
๐ 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.
๐ Key Principles
- โข All objects fall at the same rate (ignoring air resistance)
- โข Acceleration is constant: g = 9.81 m/sยฒ on Earth
- โข Velocity increases linearly with time
- โข Distance increases with the square of time
๐ Galileo's Discovery
- โข Disproved Aristotle's claim about mass affecting fall rate
- โข Demonstrated with balls of different masses
- โข Led to Newton's laws of motion
- โข 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.
๐งฎ Free Fall Equations
Time to Fall
Example: Object dropped from 100m on Earth
t = โ(2 ร 100 / 9.81) = 4.52 seconds
Impact Velocity
Example: Same 100m drop
v = โ(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 = vโยฒ/(2g)
Total air time (thrown up):
t_total = 2vโ/g
โฐ When to Use This Calculator
๐ Education
- โข Physics homework and labs
- โข Understanding gravity concepts
- โข Comparing planetary physics
- โข Energy conservation demonstrations
โ๏ธ Engineering
- โข Drop testing calculations
- โข Impact force estimation
- โข Safety engineering
- โข Aerospace applications
๐ฌ Entertainment
- โข Stunt calculations
- โข Skydiving planning
- โข Bungee jump design
- โข Special effects physics
๐ช Gravity Across the Solar System
| Body | Gravity (m/sยฒ) | % of Earth | Fun Fact |
|---|---|---|---|
| ๐Earth | 9.81 | 100% | |
| ๐Moon | 1.62 | 17% | You could jump 6x higher! |
| ๐ดMars | 3.71 | 38% | Similar to 3 floors up on Earth |
| ๐ Jupiter | 24.79 | 253% | You'd weigh 2.5x more |
| ๐กVenus | 8.87 | 90% | |
| โชMercury | 3.70 | 38% | |
| ๐ชSaturn | 10.44 | 106% | |
| ๐ตUranus | 8.69 | 89% | |
| ๐Neptune | 11.15 | 114% | |
| โซPluto | 0.62 | 6% |
๐ Related Calculators
Calculate velocity, speed, and motion
Analyze projectile trajectories
Calculate terminal velocity with drag
Free fall with air resistance
Calculate kinetic energy
Calculate momentum (p = mv)
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 + vโยฒ/(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.
๐ Official Data Sources
โ ๏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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