Theory
Let us assume there is an object in free fall. To make the mathematics easier to cope with, we may also assume that air resistance does not affect the fall of our object.
The fall of the object is determined by the standard gravity [[$ g $]] of Earth. It can be deduced that after falling for a period of time [[$ t $]], the height of the fall [[$ s $]] is given by the formula:
[[$$ s = \frac{1}{2}gt^2 \quad $$]]
Let us solve this for standard gravity [[$ g $]]. Using algebra, or equation-solving, we get
[[$$ s = \frac{1}{2}gt^2 \quad ||\cdot 2 $$]]
[[$$ 2s = gt^2 \quad ||:t^2 $$]]
[[$$ \frac{2s}{t^2} = g \quad$$]]
[[$$ g = \frac{2s}{t^2} \quad$$]]
The fall of the object is determined by the standard gravity [[$ g $]] of Earth. It can be deduced that after falling for a period of time [[$ t $]], the height of the fall [[$ s $]] is given by the formula:
[[$$ s = \frac{1}{2}gt^2 \quad $$]]
Let us solve this for standard gravity [[$ g $]]. Using algebra, or equation-solving, we get
[[$$ s = \frac{1}{2}gt^2 \quad ||\cdot 2 $$]]
[[$$ 2s = gt^2 \quad ||:t^2 $$]]
[[$$ \frac{2s}{t^2} = g \quad$$]]
[[$$ g = \frac{2s}{t^2} \quad$$]]