Answer
$7$ seconds.
Work Step by Step
The function modelling the height of the baseball above the ground is
$s(t)=-16t^2+48t+448$.
At time $t=0$ the ball's height above the ground is
$s(0)=-16(0)^2+48(0)+448$
$s(0)=0+0+448$
$s(0)=448$ feet.
When the ball hit the ground the height of the ball is $s(t)=0$.
$0=-16t^2+48t+448$
Divide both sides by $-16$
$\frac{0}{-16}=\frac{-16t^2}{-16}+\frac{48t}{-16}+\frac{448}{-16}$
Simplify.
$0=t^2-3t-28$
Rewrite the middle term $-3t$ as $-7t+4t$
$0=t^2-7t+4t-28$
Group terms.
$0=(t^2-7t)+(4t-28)$
Factor out from each term.
$0=t(t-7)+4(t-7)$
Factor out $(t-7)$.
$0=(t-7)(t+4)$
Set each factor equal to zero.
$t-7=0$ or $t+4=0$
Isolate $x$.
$t=7$ or $t=-4$
Take the positive value because $t\geq 0$.
Ball will take $7$ seconds to hit the ground.
