Key Takeaways
- Free fall is motion under the sole influence of gravity, with acceleration of 9.8 m/s2 on Earth
- All objects fall at the same rate regardless of mass (in a vacuum)
- Velocity increases linearly: v = v0 + gt
- Distance increases quadratically: d = v0t + (1/2)gt2
- After 5 seconds of free fall, an object reaches 49 m/s (~110 mph) and falls 122.5 meters
What Is Free Fall? Understanding Gravitational Motion
Free fall is the motion of an object where gravity is the only force acting upon it. This idealized condition assumes no air resistance, allowing us to study pure gravitational acceleration. In free fall, all objects accelerate at exactly the same rate regardless of their mass - a principle famously demonstrated by Galileo at the Leaning Tower of Pisa and later confirmed by astronauts on the Moon.
On Earth's surface, the gravitational acceleration (denoted as g) is approximately 9.8 m/s2 (or 32.2 ft/s2). This means that every second an object is in free fall, its velocity increases by 9.8 meters per second. After one second, it's moving at 9.8 m/s; after two seconds, 19.6 m/s; and so on.
Understanding free fall is fundamental to physics and has practical applications in everything from calculating building evacuation times during emergencies to designing roller coasters, understanding skydiving dynamics, and planning spacecraft maneuvers.
The Free Fall Equations Explained
v = v0 + gt
d = v0t + (1/2)gt2
v2 = v02 + 2gd
These three kinematic equations allow you to solve any free fall problem when you know at least two variables. The first equation relates velocity to time, the second relates distance to time, and the third relates velocity to distance (useful when time is unknown).
How to Calculate Free Fall (Step-by-Step)
Identify Known Variables
Determine what you know: initial velocity (v0), time (t), or distance (d). For objects dropped from rest, v0 = 0. The gravitational acceleration g = 9.8 m/s2 is constant.
Select the Appropriate Equation
Use v = v0 + gt to find velocity when you know time. Use d = v0t + (1/2)gt2 to find distance. Use v2 = v02 + 2gd when time is unknown.
Substitute Values
Plug your known values into the equation. Example: For an object dropped (v0 = 0) falling for 3 seconds: v = 0 + (9.8)(3) = 29.4 m/s
Calculate Distance
Using the same example: d = 0(3) + (1/2)(9.8)(3)2 = 0 + 0.5 x 9.8 x 9 = 44.1 meters
Verify Your Answer
Cross-check using another equation. The third equation gives: v2 = 0 + 2(9.8)(44.1) = 864.36, so v = 29.4 m/s. This confirms our velocity calculation.
Real-World Example: Dropping a Stone from a Bridge
Using d = (1/2)gt2 = 0.5 x 9.8 x 16 = 78.4 meters. The stone hits the water at 39.2 m/s (about 88 mph)!
Practical Applications of Free Fall Calculations
Free fall physics has numerous real-world applications that affect our daily lives and scientific endeavors:
Engineering and Construction
Engineers use free fall calculations to design safety systems. Building evacuation plans must account for how quickly objects or debris might fall. Elevator safety brakes are designed based on free fall physics, and construction workers use these calculations to ensure dropped tools don't endanger those below.
Sports and Recreation
Skydivers, bungee jumpers, and cliff divers all rely on understanding free fall. While air resistance is a factor in real-world scenarios, free fall equations provide the baseline for these calculations. Roller coaster designers use free fall physics to create thrilling drops while maintaining safety standards.
Space Exploration
Astronauts in orbit are actually in a continuous state of free fall around Earth. Understanding free fall is essential for spacecraft trajectory calculations, satellite deployment, and planning lunar or planetary landings where gravitational acceleration differs from Earth.
Pro Tip: Quick Mental Calculations
For rough estimates, remember these approximations: After 1 second of free fall, velocity is about 10 m/s and distance is about 5 meters. After 2 seconds: 20 m/s and 20 meters. After 3 seconds: 30 m/s and 45 meters. These round numbers make mental math much easier!
Free Fall on Different Planets
The gravitational acceleration varies significantly across celestial bodies, dramatically affecting free fall behavior:
| Celestial Body | g (m/s2) | After 3 Seconds: Velocity | After 3 Seconds: Distance |
|---|---|---|---|
| Moon | 1.62 | 4.86 m/s | 7.29 m |
| Mars | 3.71 | 11.13 m/s | 16.70 m |
| Earth | 9.81 | 29.43 m/s | 44.15 m |
| Jupiter | 24.79 | 74.37 m/s | 111.56 m |
| Sun (surface) | 274 | 822 m/s | 1,233 m |
Free Fall vs. Real-World Falling: Air Resistance
In reality, air resistance (drag) significantly affects falling objects. As an object accelerates, air resistance increases until it equals the gravitational force, resulting in terminal velocity - the maximum speed a falling object can reach.
Important: Free Fall is an Idealization
Our calculator assumes no air resistance, which is accurate for calculations in a vacuum or for initial approximations. In real-world scenarios with air, falling objects will reach terminal velocity and stop accelerating. A skydiver reaches terminal velocity of about 53 m/s (120 mph) in a spread position, much slower than free fall calculations would suggest.
The terminal velocity depends on several factors including the object's mass, shape, and surface area. A feather falls slowly due to high drag relative to its weight, while a bowling ball's terminal velocity is much higher because its weight-to-drag ratio is larger.
Common Mistakes to Avoid
When working with free fall problems, students and professionals often make these errors:
- Forgetting direction conventions: Typically, downward is positive for free fall problems, so g = +9.8 m/s2. Be consistent throughout your calculation.
- Confusing velocity and speed: Velocity is a vector (includes direction), speed is scalar (magnitude only). In free fall, velocity increases downward.
- Using the wrong equation: Match your equation to your known variables. If you don't know time, use v2 = v02 + 2gd instead of the time-dependent equations.
- Unit inconsistencies: Ensure all values are in compatible units (meters and seconds, or feet and seconds). Don't mix metric and imperial!
- Ignoring significant figures: Use g = 9.8 m/s2 for standard calculations, or g = 9.81 m/s2 for more precision. Don't report more decimal places than your inputs justify.
Related Physics Concepts
Projectile Motion
Two-dimensional motion combining horizontal velocity with vertical free fall.
Terminal Velocity
Maximum velocity reached when air resistance equals gravitational force.
Gravitational Force
The force of attraction between masses, causing acceleration toward Earth's center.
Frequently Asked Questions
In free fall (without air resistance), gravitational acceleration is independent of mass. While heavier objects experience more gravitational force, they also have more inertia. These effects cancel out exactly, causing all objects to accelerate at the same rate of 9.8 m/s2. This principle, known as the equivalence of gravitational and inertial mass, was famously demonstrated by Galileo and is a cornerstone of Einstein's General Relativity.
Drop an object and time how long it takes to hit the ground. Use the formula h = (1/2)gt2. For example, if the fall takes 3 seconds: h = 0.5 x 9.8 x 9 = 44.1 meters. For better accuracy, perform multiple trials and average the results. Note: This method works best for heights under 50 meters where air resistance has minimal effect.
g (lowercase) is the acceleration due to gravity at a specific location, like Earth's surface (9.8 m/s2). G (uppercase) is the universal gravitational constant (6.674 x 10-11 N m2/kg2), which appears in Newton's law of universal gravitation. The relationship is: g = GM/r2, where M is Earth's mass and r is the distance from Earth's center.
In pure free fall (no air resistance), after 10 seconds: v = gt = 9.8 x 10 = 98 m/s (about 219 mph or 353 km/h). You would have fallen d = (1/2)gt2 = 490 meters. However, in reality, a human body would reach terminal velocity of about 53-67 m/s (depending on body position) well before 10 seconds, typically within 10-15 seconds of falling.
In a vacuum (true free fall), no - all objects fall at exactly the same rate regardless of mass. Apollo 15 astronaut David Scott famously demonstrated this on the Moon by dropping a hammer and feather simultaneously - they hit the ground at the same time. However, in air, mass does matter because heavier objects have higher terminal velocities due to their better weight-to-drag ratio.
Gravitational acceleration decreases with altitude because you're farther from Earth's center. At sea level, g = 9.81 m/s2. At the top of Mount Everest (8,849m), g = 9.78 m/s2. At the altitude of the International Space Station (400 km), g = 8.7 m/s2. The formula is g = g0(R/(R+h))2, where R is Earth's radius and h is altitude.
Air resistance creates a drag force: Fd = (1/2)CpAv2, where C is the drag coefficient, p is air density, A is cross-sectional area, and v is velocity. The terminal velocity occurs when drag equals weight: vt = sqrt(2mg/(CpA)). For most practical calculations involving humans or common objects, you can use published terminal velocity values rather than calculating from scratch.
Yes! The same equations apply, but with a non-zero initial velocity (v0). If you throw an object downward at 5 m/s, simply use v0 = 5 m/s in your calculations. After 2 seconds: v = 5 + (9.8)(2) = 24.6 m/s, and distance = (5)(2) + (0.5)(9.8)(4) = 10 + 19.6 = 29.6 meters. The object starts faster and travels farther than if simply dropped.