If an object is thrown upward with an initial velocity of 112 feet per second, its height after t seconds is given by s(t) = 112t - 16t^2. Find the maximum height attained by the object. The object will attain maximum height exactly at the halfway point in terms of the time t, where t = 0 is at the beginning of the object's flight, and the final time is when the object hits the ground.