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.
The fence around the fair is 13 feet high but beyond the fence has a great view of the mountains.
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?