Answer
$t\approx 1.68$
Work Step by Step
Write height function.
$ h=-16t^{2}+h_{0}\qquad$ ...Substitute $0$ for $h$ and $45$ for $h_{0}$
$ 0=-16t^{2}+45\qquad$ ...add $16t^{2}$ to each side
$ 16t^{2}=45\qquad$ ...divide both sides of the expression with $16$
$ t^{2}=\displaystyle \frac{45}{16}\qquad$ ...take square roots of each side.
$ t=\pm\sqrt{\frac{45}{16}}\qquad$ ...simplify $\displaystyle \sqrt{\frac{45}{16}}=\frac{\sqrt{9\cdot 5}}{\sqrt{16}}=\frac{3\sqrt{5}}{4}$
$\qquad$ ...since we are calculating time, we can discard the negative solution
$t=\displaystyle \frac{3\sqrt{5}}{4}$
$t\approx 1.68$
