Free Fall Distance Calculator
Calculate the distance traveled by an object in free fall using time, velocity, or gravitational acceleration
Calculate Free Fall Distance
Time the object has been falling
Starting velocity (0 for objects dropped from rest)
Gravitational acceleration (9.80665 m/s² for Earth)
Unit for displaying the calculated distance
Free Fall Results
Formula used: h = v₀t + ½gt²
Input values: Time: 0.00s, Initial velocity: 0m/s, Gravity: 9.80665m/s²
Distance in meters: 0.0000 m
Physics Analysis
Example Calculations
Drop from Rest (3 seconds)
Given: t = 3s, v₀ = 0 m/s, g = 9.80665 m/s²
Formula: h = ½gt²
Calculation: h = ½ × 9.80665 × 3²
Result: h = 44.13 m
Reaching 100 m/s
Given: v = 100 m/s, v₀ = 0 m/s, g = 9.80665 m/s²
Formula: h = v² / (2g)
Calculation: h = 100² / (2 × 9.80665)
Result: h = 509.86 m
Moon Gravity (2 seconds)
Given: t = 2s, v₀ = 0 m/s, g = 1.625 m/s²
Formula: h = ½gt²
Calculation: h = ½ × 1.625 × 2²
Result: h = 3.25 m
Free Fall Equations
Distance from Time
h = v₀t + ½gt²
When fall time is known
Distance from Velocity
h = (v² - v₀²) / (2g)
When final velocity is known
Velocity from Time
v = v₀ + gt
Final velocity calculation
Time from Velocity
t = (v - v₀) / g
Time to reach velocity
Terminal Velocity
In reality, objects reach terminal velocity due to air resistance:
Gravity Comparison
Note: Earth's gravity varies slightly by location (9.764 to 9.834 m/s²)
Understanding Free Fall Motion
What is Free Fall?
Free fall is the motion of an object under the influence of gravity alone, without air resistance or other forces. In free fall, all objects accelerate downward at the same rate regardless of their mass.
Key Principles
- •Acceleration is constant and equal to gravity (g)
- •Mass doesn't affect fall time (in vacuum)
- •Distance increases quadratically with time
- •Velocity increases linearly with time
Formula Derivations
Distance Formula
Starting from: a = g (constant acceleration)
Integrating: v = v₀ + gt
Integrating again: h = v₀t + ½gt²
Energy Method
Kinetic energy: KE = ½mv²
Potential energy: PE = mgh
Energy conservation: ½mv² = mgh + ½mv₀²
Therefore: h = (v² - v₀²) / (2g)
Real-World Considerations
- ⚠️Air Resistance: Slows down objects, causes terminal velocity
- ⚠️Shape Factor: Affects drag coefficient and air resistance
- ⚠️Altitude: Gravity and air density change with height
- ⚠️Rotation: Earth's rotation affects very long falls
Common Applications
- ✓Physics Education: Understanding motion and gravity
- ✓Engineering: Designing safety systems and structures
- ✓Sports: Analyzing projectile motion in various sports
- ✓Space Science: Calculating orbital mechanics