#### Answer

19 seconds

#### Work Step by Step

We are given that the height of a projectile at any time t can be described by the polynomial function $P(t)=-16t^{2}+300t$.
In order to find how long before an object will hit the ground, we must find the value of t such that $P(t)=0$.
$0=-16t^{2}+300t$
Add $16t^{2}$ to both sides.
$16t^{2}=300t$
Divide both sides by t.
$16t=300$
Divide both sides by 16.
$t=18.75\approx19$ seconds