When rocket hit the ground the height of rocket from the ground is 0. So y = 0, when rocket hit the ground.
Simplify the equation -16x^2+248x+116 = 0 by using quadratic formula to obtain the value ot time, x.
![\begin{gathered} x=\frac{-248\pm\sqrt[]{(248)^2-4\cdot(-16)\cdot(116)}}{2\cdot(-16)} \\ =\frac{-248\pm\sqrt[]{68928}}{-32} \\ =(-248\pm262.54)/(-32) \\ =(-248-262.54)/(-32) \\ =-(510.54)/(-32) \\ =15.95 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/7wy463y88zabgwmolitnhmi5bxgvpwudut.png)
The negative value of time is neglected as time can never be negative.
Thus time at which rocket hit the ground is 15.95 seconds.