The eqution of height y in terms of the time x is
[tex]y=-16x^2+116x+7.[/tex]
We are asked when the rocket will strike the ground, so that is the same that sayin when will the rocket's height will be zero again, that is, y=0. so we have to solve
[tex]-16x^2+116x+7=0.[/tex]
the solutions of this equations are
[tex]x=\frac{-116\pm\sqrt[]{116^2-4(-16)(7)}}{2(-16)}=\mleft\{\begin{aligned}-0.05 \\ 7.3\end{aligned}\mright.[/tex]
So, the rocket will strike the ground after 7.3 seconds
