CPM Homework Help : CALC Problem 5-81

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

Starting velocity
Hint (a):
Evaluate $v(t)$ when $t = 0$ .

Starting position
Hint (b):
Evaluate $h(t)$ when $t = 0$ .

Maximum height
Hint 1(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 2(c):
The maximum height will occur at the time when $v(t) = 0$ .
Answer (c):
The vertex of the parabola is located at $t = –21/2(–4.9) ≈ 2.143$ seconds.
$h(2.143) ≈ 25.5$ m