If the height (in meters) of an object traveling vertically is represented by the function $h\left(t\right) = −4.9t^{2} + 21t + 3$ where $t$ is measured in seconds, determine its:

1. Starting velocity

   Hint (a):

   Evaluate $v\left(t\right)$ when $t = 0$.

2. Starting position

   Hint (b):

   Evaluate $h\left(t\right)$ when $t = 0.$

3. Maximum height

   Hint (c):

   Since the height function is a parabola, the maximum height can be determined by using Algebra to locate the vertex. Calculus can also be used.

   Hint (c):

   The maximum height will occur at the time when $v\left(t\right) = 0$.

   Answer (c):

   The vertex of the parabola is located at $t = –21/2\left(–4.9\right) ≈ 2.143$ seconds.
   $h\left(2.143\right) ≈ 25.5$ m