SOLUTION
The object would hit the ground at the root of the equation, that is where h = 0
So we have
[tex]\begin{gathered} h=-16t^2+32t+48=0 \\ -16t^2+32t+48=0 \\ 16t^2-32t-48=0 \\ divide\text{ through by 16} \\ t^2-2t-3=0 \end{gathered}[/tex]Solving the quadratic equation, we have
[tex]\begin{gathered} t^2-3t+t-3=0 \\ t(t-3)+1(t-3)=0 \\ (t-3)(t+1)=0 \\ t=3,\text{ or} \\ t=-1 \end{gathered}[/tex]So we ignore -1 as time cannot be negative.
Hence the object hit the ground in 3 seconds
