Final answer:
To find the maximum height attained by the ball, determine the vertex time of the quadratic equation using -b/(2a). Calculating with the provided coefficients, the ball reaches maximum height at 0.75 seconds, which is 9 feet.
Step-by-step explanation:
The student has asked about the maximum height attained by a ball thrown directly upward with a velocity of 24 feet per second, using the given height-time equation h=24t-16t^2. To find the maximum height, we need to find the vertex of the parabola represented by the equation, which in this case is a quadratic function of time (t).
We know that the vertex form of a quadratic equation ax^2 + bx + c is given by -b/(2a), where a is the coefficient of t^2 and b is the coefficient of t. Applying this to the provided equation, with a = -16 and b = 24, we can calculate the time at which the maximum height is reached:
t = -b/(2a) = -24/(2*(-16)) = 24/32 = 0.75 seconds.
Plugging t = 0.75 seconds back into the height equation, we get the maximum height of the ball: h = 24*(0.75) - 16*(0.75)^2 = 18 - 9 = 9 feet. Therefore, the ball reaches a maximum height of 9 feet.