Hi there! The answer is 11 seconds.
We want to find out when the height of the rocket equals 0 (because then it'll be on the ground). When we know this we can set up an equation.
[tex] - 16 {t}^{2} + 176t = 0[/tex]
[tex] - 16t(t - 11) = 0[/tex]
[tex] - 16t = 0 \: \: \: \: or \: \: \: \: t - 11 = 0[/tex]
[tex]t = 0 \: \: \: \ \: \: \: \: \: \: \: \: or \: \: \: \: t = 11[/tex]
Therefore the rocket will be returned in the ground after 11 seconds.
