A professional fireworks team shoots an 8-in. mortar straight upwards from ground level with an initial speed of 256 ft/sec. a. Write a function modeling the vertical position s(t) (in ft)) of the shell at a time t seconds after launch. b. The mortar is designed to explode when the shell is at its maximum height. How long after launch will the shell explode? (Hint: Consider the vertex formula from Section 3.1.) c. The spectators can see the shell rising once it clears a 200-ft tree line. For what period of time after launch is the shell visible before it explodes?