A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by $h(t)=-4.9 t^{2}+24 t+8$. How long does it take to reach maximum height?' (Round your answer to three decimal places.) s

Step 1 ：The height of the ball is given by a quadratic function. The maximum height of a quadratic function \(f(x) = ax^2 + bx + c\) is reached at the vertex of the parabola, which occurs at \(x = -\frac{b}{2a}\). In this case, \(a = -4.9\) and \(b = 24\), so we can substitute these values into the formula to find the time it takes to reach maximum height.

Step 2 ：Substitute \(a = -4.9\) and \(b = 24\) into the formula \(x = -\frac{b}{2a}\) to get \(t_{max\_height} = 2.4489795918367343\).

Step 3 ：Round the result to three decimal places to get the final answer.

Step 4 ：Final Answer: The time it takes to reach maximum height is approximately \(\boxed{2.449}\) seconds.