A pomegranate is thrown from ground level straight up into the air at time $t=0$ with velocity 128 feet per second. Its height in feet at $t$ seconds is $f(t)=-16 t^{2}+128 t$. Find the time it hits the ground and the time it reaches its highest point.
Hits the ground when $t=$ (include units)
Reaches highest point when $t=$ (include units)
Maximum height $=$ (include units)

Step 1 ：The pomegranate hits the ground when its height is zero, i.e., when \(f(t) = 0\). We can solve the equation \(-16t^2 + 128t = 0\) to find the time it hits the ground.

Step 2 ：The pomegranate reaches its highest point when its velocity is zero. The velocity is the derivative of the height function, \(f'(t) = -32t + 128\). We can solve the equation \(-32t + 128 = 0\) to find the time it reaches its highest point.

Step 3 ：The maximum height is the value of the height function at the time it reaches its highest point, i.e., \(f(t)\) at the solution of \(-32t + 128 = 0\).

Step 4 ：Final Answer: The pomegranate hits the ground when \(t = \boxed{8}\) seconds. It reaches its highest point when \(t = \boxed{4}\) seconds. The maximum height is \(\boxed{256}\) feet.