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. $$ v=\sqrt { 2gh } $$
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