A volleyball is sever a by a 6ft player at an into an 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 seconda. Using this equation, define the domain of the ball when it reaches its maximum height
To find the domain of the ball when it reaches its maximum height, we need to determine the values of t that are applicable in this situation.
The ball reaches its maximum height when it stops going upwards and starts to descend. At this point, the velocity is 0 ft/s. Using the equation h = -16t^2 + 33t + 6, we can set the velocity to 0 and solve for t:
0 = -16t^2 + 33t + 6
To solve this quadratic equation, we can either factor it, complete the square, or use the quadratic formula. Let's use the quadratic formula:
t = (-33 ± √(33^2 - 4(-16)(6))) / (2(-16))
Simplifying the equation:
t = (-33 ± √(1089 + 384)) / (-32)
t = (-33 ± √1473) / (-32)
Since time cannot be negative in this context, we can ignore the negative solution:
t = (-33 + √1473) / (-32) ≈ 1.84375
Therefore, the ball reaches its maximum height at approximately 1.84375 seconds.
The domain of the ball when it reaches its maximum height is the range of valid values for t in the context of the problem. Since it does not make sense to have negative time or time greater than the time it takes for the ball to reach its maximum height, the domain is:
0 ≤ t ≤ 1.84375