Answer
$6400$ feet
Work Step by Step
Given \begin{equation}
t=\sqrt{\frac{2 h}{32}}.
\end{equation} We are given that $t = 20$ seconds and want to find the height from which an object is dropped. Find $t = 20$ and solve for $h$. \begin{equation}
\begin{aligned}
20 & = \sqrt{\frac{2 h}{32}} \\
(20)^2&=\left( \sqrt{\frac{2 h}{32}} \right)^2\\
400& = \frac{2h}{32}\\
\frac{400\cdot 32}{2}& = h\\
6400&= h.
\end{aligned}
\end{equation} The object must be dropped from a height of $6400$ feet.
