The Mechanics of Free Fall
Free fall is a specific state of motion where an object is falling under the sole influence of gravity. In an idealized physics model, this means there is zero air resistance, no friction, and no other external forces acting upon the object.
One of the most profound discoveries in classical mechanics—famously demonstrated by Galileo dropping spheres from the Leaning Tower of Pisa—is that all objects in free fall accelerate at the exact same rate, regardless of their mass. A massive iron cannonball and a tiny wooden marble will fall at the exact same speed if dropped simultaneously in a vacuum.
The Rate of Acceleration
On Earth, this universal rate of acceleration, denoted by the symbol $g$, is approximately $9.80665 , \text{m/s}^2$.
This means that for every single second an object is falling, its velocity increases by $9.8$ meters per second.
- At $t = 0\text{s}$, velocity is $0 , \text{m/s}$.
- At $t = 1\text{s}$, velocity is $9.8 , \text{m/s}$.
- At $t = 2\text{s}$, velocity is $19.6 , \text{m/s}$, and so on.
Calculating Free Fall Velocity and Distance
Because free fall is a scenario of constant acceleration, we can use standard kinematic equations to determine exactly how fast the object is moving and how far it has fallen at any given moment in time.
The Formulas
To find the Final Velocity ($v$) and the Distance Fallen ($d$) after a specific amount of Time ($t$):
Example Calculation
Imagine you drop a rock off a very tall cliff and count exactly $5$ seconds before it hits the ground.
- Velocity upon impact: $v = 9.80665 \cdot 5 = \mathbf{49.03 , \text{m/s}}$ (which is roughly $110 , \text{mph}$).
- Height of the cliff (Distance fallen): $d = \frac{1}{2} \cdot 9.80665 \cdot (5^2) = \frac{1}{2} \cdot 9.80665 \cdot 25 = \mathbf{122.58 , \text{meters}}$.
Real-World Limitations
It is critical to remember that true free fall only exists in a vacuum. If you jump out of an airplane, you are not in true free fall because you are crashing into billions of air molecules as you descend. This creates aerodynamic drag (air resistance) pushing up against you. Eventually, the upward drag force will equal the downward force of gravity, and you will stop accelerating. This maximum speed is known as Terminal Velocity.