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
1.22 seconds
1.22 seconds
23.01 feet
23.01 feet
−1.03 seconds
negative 1.03 seconds
1.03 seconds
To find the domain of the ball when it reaches its maximum height, we need to determine the time at which the ball reaches its maximum height.
The equation for the height of the ball is h = -16t^2 + 33t + 6.
To find the time at which the ball reaches its maximum height, we need to find the vertex of the quadratic equation. The vertex of a quadratic equation in the form y = ax^2 + bx + c can be found using the formula x = -b/2a.
In this case, a = -16 and b = 33.
x = -b/2a = -33/(2*(-16)) = 33/32 ≈ 1.03 seconds.
Therefore, the time at which the ball reaches its maximum height is approximately 1.03 seconds.
So, the domain of the ball when it reaches its maximum height is 1.03 seconds.
Therefore, the correct answer is: 1.03 seconds.