Answer
(a) $0.19\ and \ 10.92\ sec$
(b) $11.32\ sec$.
Work Step by Step
(a) Given $s=-2.7t^2+30t+6.5$, let $s=12$, we have $12=-2.7t^2+30t+6.5$ or $2.7t^2-30t+5.5=0$ which can be solved using the quadratic formula to get $t\approx0.19\ and \ 10.92\ sec$
(b) For reaching the surface, we have $s=0$, thus $0=-2.7t^2+30t+6.5$ or $2.7t^2-30t-6.5=0$ which gives $t\approx11.32\ sec$. (Discard the negative answer.)
