SPITWADS, Part Two

Marisol has more questions about her spitwad from problem 5-1.

1. How high is the spitwad after half a second? How fast is it traveling at that instant?

   Hint (a):

   Use the equation, $h\left(t\right)$, that you found in problem 5-1 to find the height of the spitwad after $2$ seconds.

   Hint (a):

   'How fast' could refer to velocity or speed. Be sure that you are clear in your answer.

2. When is the spitwad $10$ feet high? What is its velocity at those times?

   Hint (b):

   $x\left(t\right) = 10$

3. As the spitwad is falling back toward Marisol, does it ever fall at a rate of $10$ ft/sec? If so, when?

   Hint (c):

   $v\left(t\right) = −10$

   Answer (c):

   $(\text{show steps})=\frac{37}{16}\text{ seconds}$

4. How long does the spitwad take to reach its highest point? How high does it go? Determine your answer both graphically and analytically.

   Hint (d):

   The spitwad will be at its highest point at the moment when its velocity changes from positive to negative.