📂Physics

Derivation of the Formula for the Velocity of a Falling Object

Formulas

$g$ Let’s denote gravity acceleration. If an object falls from a high place to a lower one due to gravity, the formula for the velocity of this object as a function of the fallen distance $h$ is as follows. $$v=\sqrt { 2gh }$$

Derivation

Let’s ignore any conditions that are irrelevant to what we’re trying to find.

Assuming an object was at rest and then falls a distance $h$, let’s denote its velocity as $v$. Since mechanical energy is conserved, $$\frac { 1 }{ 2 }mv^{ 2 }=mgh$$ Multiplying both sides by $\displaystyle \frac { 2 }{ m }$ and taking the root gives us the following. $$v=\sqrt { 2gh }$$

■