A soccer ball is kicked from the ground with an initial upward velocity of 80 feet per second. The equation $h(t)=-16 t^{2}+80 t$ gives the height $h$ of the ball after $t$ seconds. a) Find the maximum height of the ball. \[ h_{\max }= \] feet b) How may seconds will it take for the ball to reach the ground? \[ t= \] seconds

Step 1 ：The maximum height of the ball can be found by finding the vertex of the parabola represented by the equation \(h(t)=-16 t^{2}+80 t\). The x-coordinate of the vertex of a parabola given by the equation \(y=ax^2+bx+c\) is \(-\frac{b}{2a}\). In this case, \(a=-16\) and \(b=80\), so the time at which the ball reaches its maximum height is \(-\frac{80}{2(-16)}\).

Step 2 ：We can then substitute this value back into the equation to find the maximum height. The maximum height of the ball is \(h_{max} = -16*(2.5)^2 + 80*2.5 = 100\) feet.

Step 3 ：The ball reaches the ground when \(h(t) = 0\). We can find the time it takes for the ball to reach the ground by solving the equation \(-16t^2 + 80t = 0\) for \(t\). The solutions are \(t = 0\) and \(t = 5\) seconds. Since the ball starts from the ground at \(t = 0\), it will reach the ground again at \(t = 5\) seconds.

Step 4 ：Final Answer: The maximum height of the ball is \(\boxed{100}\) feet and it will take \(\boxed{5}\) seconds for the ball to reach the ground.