Carol threw an eraser straight up with a starting velocity of $12$ m/sec and a starting height of one meter.

1. How high was the eraser after $1$ second? After $2$ seconds?

   Hint (a):

   Notice that the units are in meters, not feet. Which generic falling object (in earth) equation should we use?
   $s(t)=-\frac{32}{2}t^{2}+v_{0}t+s_{0}$ or $s(t)=-\frac{9.8}{2}t^{2}+v_{0}t+s_{0}$

   Step 1(a):

   Set up the generic falling object (on Earth) equation, plugging in values for initial velocity, $v_0$; and initial position, $s_0$.

   Step 2(a):

   Evaluate at $t = 1$ and $t = 2$.

2. When did the eraser reach its maximum height? What was the maximum height?

   Hint 1(b):

   Optimize the position.

   Hint 2(b):

   Be sure to answer both questions.