UNIT & ASSESSmENT: SAND CASTLES Oceana is a professional sand castle builder in Newport Beach. The problem is that the sand castles take forever to build so she has to plan her builds and location with tides. The gravitational pull affects the tides, creating a swell and changing how far the water comes onto the beach. High tide is when the ocean water rises higher on the beach, leaving less sandy area. Low tide is when the water is lower, leaving more sandy area. The tide follows the equation w(t) = 20sin(29t) where w(t) represents how far the waterline is above or below the average position and t, represents the number of hours elapsed since midnight. * S 1. Create a graph of the waterline for a 24-hour period. What does each piece of the equation represent? 2. What is the highest position on the beach (compared to its average position) that the waterline will have during the day (high tide)? What is the lowest position that the waterline will be during the day (low tide)? 3. Suppose Oceana plans to build her castle on the average waterline just as the water has moved below that line. How much time will she have to build before the water returns and destroys her work? 4. Suppose Oceana wants to build 10 feet below the average waterline. What is the maximum amount of time she can have for making her castle? 5. Suppose Oceana decides she needs only two hours to build her castle. What is the lowest position on the beach where she can build?