Question

A volleyball player served by a 6-foot player at an initial upward velocity of 33 feet per second. It is modeled by the equation h = -16t^2 + 33t +6 h h represents the height in feet and t represents the time in seconds. Define the domain of the ball when it reaches its maximum height

1. -1.03 seconds
2. 1.03 seconds
3. 1.22 seconds
4. 23.01 feet

Answer 1

To find the time when the volleyball reaches its maximum height, we can use the vertex formula for a quadratic equation in the form \(h(t) = -16t^2 + 33t + 6\). The maximum height occurs at the vertex of this parabola.

The formula to find the time at which the maximum height occurs in a quadratic equation \(ax^2 + bx + c\) is given by:

\[
t = -\frac{b}{2a}
\]

In this equation, \(a = -16\) and \(b = 33\).

Let's plug in the values:

\[
t = -\frac{33}{2(-16)} = -\frac{33}{-32} = \frac{33}{32} \approx 1.03 \text{ seconds}
\]

Now that we have this value, we can define the domain of the ball when it reaches its maximum height as the interval from \(t=0\) (the time the ball is served) to this maximum height time \(t \approx 1.03\) seconds.

Therefore, the correct choice for the time domain when the ball reaches its maximum height is:

**2. 1.03 seconds**.