A volleyball is served by a 6-foot player at an initial upward velocity of 33 feet per second. The situation is modeled by the equation h = −16t^2 + 33t + 6 h representing the height in feet and t representing the time in seconds. Using this equation, define the domain of the ball when it reaches its maximum height.

Question

A) 1.03 seconds
B) -1.03 seconds
C) 1.22 seconds
D) 23.01 feet

Answer 1

To find the time when the volleyball reaches its maximum height, we need to determine the vertex of the parabolic equation given by:

\[ h(t) = -16t^2 + 33t + 6 \]

The time at which the maximum height occurs for a parabolic function \(h(t) = at^2 + bt + c\) can be found using the formula:

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

In this case, \(a = -16\) and \(b = 33\). Plugging these values into the formula gives:

\[ t = -\frac{33}{2 \times -16} = \frac{33}{32} \approx 1.03125 \text{ seconds} \]

Rounding this to two decimal places gives approximately \(1.03\) seconds.

Therefore, the answer to the question, which defines the domain of the ball when it reaches its maximum height, is:

A) 1.03 seconds