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 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
23.01 feet
23.01 feet
1.03 seconds
1.03 seconds
1.22 seconds
1.22 seconds
−1.03 seconds
ALL ANSWERS:
1) 1.03 Seconds
2) 5
3) (-2, 44)
4) (0, 0) and (60, 0)
5) (2, 6)
Hope this helps
Nobody is still right as of November 2023 except for the second one. It's 2 instead of 5.
Thank you, Nobody!
To find the time at which the volleyball reaches its maximum height, we need to determine the vertex of the parabola described by the equation \( h = -16t^2 + 33t + 6 \). Since this is a quadratic equation in standard form \( h = at^2 + bt + c \), the time at which the maximum height is achieved is found by using the vertex formula for time, which is \( t = -\frac{b}{2a} \).
In the given equation, \( a = -16 \) and \( b = 33 \). So the time at which the volleyball reaches its maximum height is:
\( t = -\frac{b}{2a} = -\frac{33}{2(-16)} = \frac{33}{32} \)
\( t = 1.03125 \) seconds
This time is the value at the peak of the parabola where the maximum height is reached, and it serves as the domain value that corresponds to the maximum height. Hence, the correct answer from the provided options is:
1.03 seconds
The other options are incorrect with respect to the domain of the ball when it reaches its maximum height, as:
- "23.01 feet" and "−1.03 seconds" are not related to the domain which is the time.
- "1.22 seconds" is not the correct time for when the ball reaches its maximum height given the provided equation.