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=−16t2+33t+6

Question

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.(1 point)
Responses

1.22 seconds
1.22 seconds

−1.03 seconds
negative 1.03 seconds

23.01 feet
23.01 feet

1.03 seconds
1.03 seconds
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Answer 1

To find the time when the volleyball reaches its maximum height, you can use the vertex formula for a quadratic equation, which is given by \( t = -\frac{b}{2a} \), where the quadratic equation is in the form \( h(t) = at^2 + bt + c \).

In your equation, \( h = -16t^2 + 33t + 6 \):

• \( a = -16 \)
• \( b = 33 \)

Now, plug in the values into the vertex formula:

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

This means that the ball reaches its maximum height at approximately 1.03 seconds.

Now, since we are looking for the domain of the ball as it reaches its maximum height, we should note that it only makes sense in the context of positive time (t >= 0) when considering this physical scenario. Hence, the domain of the ball when it reaches its maximum height would generally be:

Domain of the ball when it reaches maximum height: \( t \in [0, 1.03] \) seconds.

In the options you've provided, the closest specific response to when it reaches its maximum height is:

1.03 seconds.