Answer: if S is the distance, the fact that the distance is proportional to the square of the time means that S(t) = a*[tex]t^{2}[/tex] where a is a constant of proportionality, with units of [tex]\frac{feet}{s^{2} }[/tex].
We know that S(1) = 16 feet = a*1, then a = 16[tex]\frac{feet}{s^{2} }[/tex]
then S(2) = 16*4 feet = 64.
and if we want to know in how much time te objet will fall 400feet, then S(t₀) = 400 feet = 16*[tex]t₀^{2}[/tex]
so t₀ = [tex]\sqrt{400/16}[/tex] = 5s.
