If an object is projected upward from ground level with an initial velocity of $112 \mathrm{ft}$ per sec, then its height in feet after $t$ seconds is given by $s(t)=-16 t^{2}+112 t$. Find the number of seconds it will take to reach its maximum height. What is this maximum height?

Step 1 ：The height of the object is given by a quadratic function. The maximum height is reached at the vertex of the parabola represented by this function. For a quadratic function in the form \(f(t) = at^2 + bt + c\), the \(t\) value of the vertex can be found using the formula \(t = -b/2a\). In this case, \(a = -16\) and \(b = 112\). So, we can calculate \(t\) using these values.

Step 2 ：\[a = -16\]

Step 3 ：\[b = 112\]

Step 4 ：\[t = -\frac{b}{2a} = 3.5\]

Step 5 ：The time it takes for the object to reach its maximum height is 3.5 seconds. Now, to find the maximum height, we can substitute this value of \(t\) into the equation for \(s(t)\).

Step 6 ：\[s = -16t^2 + 112t\]

Step 7 ：Substitute \(t = 3.5\) into the equation

Step 8 ：\[s = -16(3.5)^2 + 112(3.5) = 196.0\]

Step 9 ：Final Answer: The object will reach its maximum height after \(\boxed{3.5}\) seconds. This maximum height is \(\boxed{196.0}\) feet.