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.
• 23.01 feet
• -1.03 seconds
• 1.22 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 height is maximized.
The equation h = -16t² + 33t + 6 represents the height as a function of time.
To find the maximum height, we can use the vertex formula x = -b/2a, where x represents the time at the vertex (maximum point) of the parabola, a represents the coefficient of the t² term (-16 in this case), and b represents the coefficient of the t term (33 in this case).
In this case, a = -16 and b = 33.
Using the vertex formula, we have:
t = -33 / (2 * -16)
t = -33 / -32
t = 1.03 seconds
Therefore, the time at which the ball reaches its maximum height is 1.03 seconds.
Now we need to find the height at this time. We can substitute t = 1.03 into the equation:
h = -16(1.03)² + 33(1.03) + 6
h = -16(1.0609) + 33.99 + 6
h = -17.0576 + 33.99 + 6
h = 23.01 feet
Therefore, the ball reaches its maximum height of 23.01 feet at 1.03 seconds.
The domain of the ball when it reaches its maximum height is:
1.03 seconds