Answer
The ball will be in the air for about $3.14$ seconds.
Work Step by Step
Write height model.
$h=-16t^{2}+v_{0}t+h_{0} \qquad$ ...substitute $3$ for $h, 50$ for $v_{0},$ and $4$ for $h_{0}$ .
$ 3=-16t^{2}+50t+4\qquad$ ...add $-3$ to each side.
$ 3-3=-16t^{2}+50t+4-3\qquad$...simplify.
$ 0=-16t^{2}+50t+1\qquad$ ...write in standard form.
$ 16t^{2}-50t-1=0\qquad$ ...use the Quadratic formula: $x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$ t=\displaystyle \frac{-(-50)\pm\sqrt{(-50)^{2}-4(16)(-1)}}{2(16)}\qquad$...simplify.
$ t=\displaystyle \frac{50\pm\sqrt{2564}}{32}\qquad$...simplify.
...since we are calculating time, we can discard the negative solution.
$ t=\displaystyle \frac{25+\sqrt{641}}{16}\qquad$...use calculator
$t\approx 3.14$.
