On the moon, the acceleration due to gravity is about $–5 \text{ ft/s}^2$. An astronaut jumps into the air with an initial upward velocity of $12$ ft/s.

1. How long is the astronaut off the ground?

   Hint (a):

   $s(t)=\frac{1}{2}at^{2}+v_{0}t+s_{0}$

   Hint (a):

   What do the zeros of $s\left(t\right)$ represent?

2. How far off the ground does the astronaut rise?

   Hint (b):

   Find the $y$-value of the vertex of $s(t)$. You can use Algebra or Calculus.