What is Free Fall?
In physics, **free fall** is the motion of an object where gravity is the only force acting upon it. In a true free fall, an object accelerates downwards at a constant rate, denoted by $g$. On Earth, this acceleration due to gravity is approximately **9.8 m/s²** (or 32.2 ft/s²).
These calculators ignore the effects of air resistance. In the real world, air resistance (or drag) opposes the motion and can significantly alter the results, especially for light objects or at high speeds. In a vacuum (like on the moon), a feather and a hammer dropped from the same height will hit the ground at the exact same time, as famously demonstrated by the Apollo 15 astronauts.
The Kinematic Equations for Free Fall
The motion of an object in free fall can be described by three primary kinematic equations. These equations relate the five key variables: distance ($d$), time ($t$), initial velocity ($v_i$), final velocity ($v_f$), and acceleration ($g$).
1. Velocity from Time
This formula calculates the final velocity of an object based on its initial velocity and the time it has been falling.
2. Distance from Time
This formula calculates the total distance an object has fallen based on its initial velocity and the time elapsed.
3. Velocity from Distance
This "timeless" equation is very useful as it calculates the final velocity of an object without needing to know the time it took to fall.
Special Case: Dropped from Rest
The most common free fall scenario involves an object being **dropped from rest**. In this case, the initial velocity ($v_i$) is 0. This greatly simplifies the equations:
- $v_f = (0) + gt \implies$
- $d = (0)t + \frac{1}{2}gt^2 \implies$
- $v_f^2 = (0)^2 + 2gd \implies$
These simpler formulas are what our calculators use when you enter an initial velocity of 0. For example, if you drop a rock from a cliff (initial height $h$), you can find its potential energy ($PE=mgh$), and as it falls, that energy is converted into kinetic energy ($KE = \frac{1}{2}mv^2$). Using $v_f^2 = 2gd$, you can see that $gh = \frac{1}{2}v_f^2$, which perfectly demonstrates the conservation of energy ($mgh = \frac{1}{2}mv_f^2$).
For a deeper dive into the physics of motion, the Wikipedia article on the equations of motion is an excellent resource.