### Home > CALC > Chapter 5 > Lesson 5.2.3 > Problem5-81

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:

1. Starting velocity

Evaluate $v(t)$ when $t = 0$.

1. Starting position

Evaluate $h(t)$ when $t = 0$.

1. Maximum height

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.

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

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