Select the correct answer.

A volleyball player sets a volleyball straight up into the air. The height of the volleyball, [tex]h(t)[/tex], is modeled by this equation, where [tex]t[/tex] represents the time, in seconds, after the ball was set.

[tex]
h(t) = -16t^2 + 20t + 6
[/tex]

The volleyball reaches its maximum height after 0.625 seconds. What is the maximum height of the volleyball?

A. 12.25 feet
B. 8.5 feet
C. 1.625 feet
D. 11.625 feet



Answer :

To determine the maximum height of the volleyball, we need to evaluate the given height function at the time when it reaches its maximum height. The height function is given by:

[tex]\[ h(t) = -16t^2 + 20t + 6 \][/tex]

We are told that the volleyball reaches its maximum height at [tex]\( t = 0.625 \)[/tex] seconds. To find the corresponding height at this moment, we simply substitute [tex]\( t = 0.625 \)[/tex] into the equation:

[tex]\[ h(0.625) = -16(0.625)^2 + 20(0.625) + 6 \][/tex]

Upon evaluation, we find that:

[tex]\[ h(0.625) = 12.25 \][/tex]

Therefore, the maximum height of the volleyball is:
[tex]\[ \boxed{12.25 \text{ feet}} \][/tex]

Hence, the correct answer is:

A. 12.25 feet