D. 5.4 seconds
1) Since the course of that ball is described by the function h(t) = -16t² +86t +4.
So we can sketch out:
When the ball hits the ground, we'll have to find out the 2nd root of that function since when t=0, h =4. So let's find out the roots:
[tex]\begin{gathered} h(t)\text{ =-16t²+86t+4} \\ \Delta=(86)^2-4(-16)(4) \\ \Delta=7396+256 \\ x=\frac{-86\pm\sqrt[]{7652}}{2(-16)} \\ x_1=5.42 \\ x_2=-0.046 \end{gathered}[/tex]3) Since just the positive answer is interesting, then we can state that the answer is D (rounded off to the nearest tenth
