Answer
$4.1$ seconds
Work Step by Step
We are given that $ s(t)=-16t^2+64t+5$
Set $ s(t)=0$
Now, $-16t^2+64t+5=0$
This implies that $ t= \dfrac{-64 \pm \sqrt {(64)^2-4\times (-16) \times 5}}{2 \times (-16)}$
$ t \approx -0.1, 4.1$
Neglect the negative value (because it does not make sense to have negative time).
Thus, our result is: $ t \approx 4.1$ seconds
Thus, the ball hits the ground after about $4.1$ seconds.
