Okay, here we have this:
Considering the provided infotmation, we are goning to calculate the requested time, so we obtain the following:
So we will set the function equal to zero and solve for t, we have:
[tex]\begin{gathered} (\frac{1}{2})32t^2+16t=480 \\ (\frac{1}{2})32t^2+16t-480=0 \\ 16t^2+16t-480=0 \\ t_{1,2}=\frac{-16\pm\sqrt{16^2-4(16)(-480)}}{2(16)} \\ t_{1,2}=\frac{-16\pm\sqrt{16^2+30720}}{32} \\ t_{1,2}=\frac{-16\pm\sqrt{256+30720}}{32} \\ t_{1,2}=\frac{-16\pm176}{32} \\ t_1=\frac{-16+176}{32},t_2=\frac{-16-176}{32} \\ t_1=\frac{160}{32},t_2=\frac{-192}{32} \\ t_1=5,t_2=-6 \end{gathered}[/tex]
Finally we obtain that The ball will take 5 seconds to hit the ground.
