Answer
The egg container will fall for about $1.37$ seconds.
Work Step by Step
$\qquad$ ...write height function.
$ h=-16t^{2}+h_{0}\qquad$ ...substitute for $h$ and $30$ for $h_{0}$.
$ 0=-16t^{2}+30\qquad$ ...add $-30$ to each side.
$ 0-30=-16t^{2}+30-30\qquad$ ...simplify.
$-30=-16t^{2}\qquad$ ...divide each side by $-16$
$\displaystyle \frac{30}{16}=t^{2}\qquad$ ...take square roots of each side.
$\pm\sqrt{\frac{30}{16}}=t\qquad$ ...apply the Quotient Property:$\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$
$ t=\displaystyle \pm\frac{\sqrt{30}}{\sqrt{16}}\qquad$ ...simplify.($\sqrt{16}=4$).
...since we are calculating time, we can discard the negative solution.
$t=\displaystyle \frac{\sqrt{30}}{4}$
$t\approx 1.37s$
