h = -16t² + 64t + 64
We want to know at what time the stone falls into the lake. If the stone is in the lake, its height is zero.
-16t² + 64t + 64 = 0
Applying the quadratic formula:
[tex]\begin{gathered} t_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t_{1,2}=\frac{-64\pm\sqrt[]{64^2-4\cdot(-16)\cdot64}}{2\cdot(-16)} \\ t_{1,2}=\frac{-64\pm\sqrt[]{8192}}{-32} \\ t_1=\frac{-64+90.5}{-32}=-0.83 \\ t_2=\frac{-64-90.5}{-32}=4.83 \end{gathered}[/tex]The negative result has no sense in the context of the problem. Then, it takes 4.83 seconds for the stone to fall into the lake
