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=−16t^2 +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
−1.03 seconds
23.01 feet
23.01 feet
1.03 seconds
1.03 seconds
1.22 seconds
The domain of the ball when it reaches its maximum height can be found by analyzing the equation representing the height of the ball.
The height equation is h = -16t^2 + 33t + 6.
To find the time at which the ball reaches its maximum height, we can use the formula for the x-coordinate of the vertex of a quadratic equation, given by:
t = -b/2a
In this case, a = -16 and b = 33.
Substituting these values into the formula, we get:
t = -33 / (2 * -16)
Simplifying this expression gives:
t = -33 / -32
t ≈ 1.03 seconds
Therefore, the domain of the ball when it reaches its maximum height is 1.03 seconds.
The correct response is: 1.03 seconds.