Step 1 :A ball is thrown upward with an initial velocity of 32 ft/sec from a height of 768 ft. Its height s, in feet, after t seconds is given by \(s=-16 t^{2}+32 t+768\). We need to find out after how long will the ball reach the ground.
Step 2 :The ball reaches the ground when its height is 0. So, we need to solve the equation \(-16t^2 + 32t + 768 = 0\) for t.
Step 3 :The solutions to the equation are -6 and 8. However, time cannot be negative, so we discard -6.
Step 4 :Final Answer: The ball will reach the ground after \(\boxed{8}\) seconds.