Free Fall Calculator
Calculate motion under gravity using kinematic equations. Our physics calculator determines velocity, time, height, and distance for free fall and projectile motion with support for different gravitational environments.
Last updated: December 15, 2024
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Results
Final Velocity
14.01 m/s
Fall Time
1.43 s
Distance
10.00 m
Formula Used:
v = √(2gh), t = √(2h/g)
Analysis:
Object falls 10m and reaches final velocity after 1.43 seconds
Free Fall Physics:
- • Acceleration due to gravity is constant (9.81 m/s² on Earth)
- • Air resistance is ignored in these calculations
- • Initial velocity is zero unless specified (projectile motion)
- • Energy is conserved: PE = mgh, KE = ½mv²
Quick Example Result
Object dropped from 10 meters on Earth (g = 9.81 m/s²):
Final Velocity
14.01 m/s
Fall Time
1.43 s
Distance
10.0 m
How This Calculator Works
Our free fall calculator uses fundamental kinematic equations from classical physics to analyze motion under gravitational acceleration. The calculations apply Newton's laws of motion and universal gravitation principles to predict object behavior during free fall and projectile motion.
Key Kinematic Equations
v = gt (velocity from time)h = ½gt² (distance from time)v² = 2gh (velocity from height)h = v²/(2g) (height from velocity)These equations assume zero initial velocity (dropped, not thrown) and neglect air resistance. For projectile motion with initial velocity, additional vector components apply.
Shows gravitational acceleration and velocity vectors
Physics Foundation
Free fall motion follows Galileo's principle that all objects fall at the same rate in a vacuum, regardless of mass. The gravitational acceleration (g) varies by celestial body and provides constant downward acceleration. Our calculator accounts for different planetary environments and converts between various unit systems for practical applications.
- Gravitational acceleration is constant for each celestial body
- Air resistance is negligible for dense objects at moderate heights
- Energy conservation: potential energy converts to kinetic energy
- Projectile motion follows parabolic trajectories under gravity
- Terminal velocity occurs when air resistance equals gravitational force
- Multiple planetary environments supported for space applications
Sources & References
- Physics: Principles and Problems - McGraw-Hill EducationStandard high school physics textbook covering kinematics
- University Physics - Young and Freedman (15th Edition)Comprehensive university-level physics reference
- NASA Planetary Fact Sheets - Gravitational data for celestial bodiesOfficial gravitational acceleration values for planets and moons
Exploring more physics? Try our concavity calculator for mathematical analysis and end behavior calculator for function limits.
Get Custom Physics Calculator for Your PlatformExample Physics Calculation
Given Values:
- Height: 381 meters
- Initial velocity: 0 m/s (dropped)
- Gravity: 9.81 m/s² (Earth)
- Air resistance: Neglected
Calculation Steps:
- Use v² = 2gh for final velocity
- v² = 2 × 9.81 × 381 = 7,472.22
- v = √7,472.22 = 86.44 m/s
- Use t = √(2h/g) for fall time
- t = √(2 × 381 / 9.81) = 8.81 seconds
Result: Final velocity = 86.44 m/s (193.5 mph), Fall time = 8.81 seconds
This demonstrates why fall protection is critical at high altitudes!
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