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

−1.03 seconds
negative 1.03 seconds

23.01 feet
23.01 feet

1.22 seconds
1.22 seconds

1.03 seconds

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

For a quadratic equation of the form \( h(t) = at^2 + bt + c \):

• The time \( t \) at which the maximum height occurs can be calculated using the formula: \[ t = -\frac{b}{2a} \] where \( a = -16 \) and \( b = 33 \).

Plugging in the values: \[ t = -\frac{33}{2 \times -16} = \frac{33}{32} \approx 1.03 \text{ seconds} \]

The height at this time can also be calculated, but since the question asks for the domain of the ball when it reaches its maximum height, we need to look at the time frame around \( t \).

Since the ball is served, and we're considering the time from 0 seconds (when it's served) until it reaches maximum height at approximately 1.03 seconds, the domain of the function (in the context of the height being analyzed) would be from \( t = 0 \) to \( t \approx 1.03 \) seconds.

Therefore, to answer the question correctly as per the given options, the time when it reaches maximum height is:

1.03 seconds.