Aball is thrown into the air with an initial velocity of 20 meters per second. The height of the ball (in meters) can be modeled by the quadratic function h(t)= time in seconds. Determine the maximum height the ball reaches and the time it takes to reach that height. The maximum height is square meters, after square seconds.

To determine the maximum height the ball reaches and the time it takes to reach that height, we need to analyze the given quadratic function for height, $h(t)$.<br /><br />The quadratic function for height is given by:<br />$h(t) = -4.9t^2 + 20t$<br /><br />To find the maximum height, we need to find the vertex of the parabola. The vertex of a parabola in the form $y = ax^2 + bx + c$ is given by the formula:<br />$x = -\frac{b}{2a}$<br /><br />In this case, $a = -4.9$ and $b = 20$, so the time at which the maximum height occurs is:<br />$t = -\frac{20}{2(-4.9)} = \frac{20}{9.8} \approx 2.04$ seconds<br /><br />Now, we can substitute this value of $t$ back into the height function to find the maximum height:<br />$h(2.04) = -4.9(2.04)^2 + 20(2.04) \approx 20.4$ meters<br /><br />Therefore, the maximum height the ball reaches is approximately 20.4 meters, and it takes about 2.04 seconds to reach that height.