Question

Two identical objects A and B fall from rest from different heights to the ground. If object B takes twice as long as A to reach the ground, what is the ratio of the heights (A:B) from which the two objects fell? Neglect air resistance.

Answer 1

using the data of your problem, we can write:
\[\Large {t_A} = \sqrt {\frac{{2{h_A}}}{g}} ,\quad {t_B} = \sqrt {\frac{{2{h_B}}}{g}} = 2{t_A}\]

Answer 2

so we get:
\[\Large \frac{{{t_A}}}{{{t_B}}} = \frac{{{t_A}}}{{2{t_A}}} = \frac{1}{2} = \sqrt {\frac{{2{h_A}}}{g}} \times \sqrt {\frac{g}{{2{h_B}}}} = \sqrt {\frac{{{h_A}}}{{{h_B}}}} \]