You are the Captain of MS Hipparchus, a Suezmax container ship that carries up to 10,000 containers. The MS Hipparchus has an air draft of 67m. The air draft means that the height
from the water line to the highest point on the ship.

Container ships docking at the Port of New York and New Jersey traverse the Kill van Kull,
passing under the Bayonne Bridge between Staten Island and Bayonne before they dock at the
container ports in Newark Bay. The deck of the bridge is 66m above Sea Level, but because of
the tides, the surface of the water can be above or below Sea Level. You have information on
the tides in the Kill van Kull that shows that on May 3, 2021, there is a high tide of 2.9m
(relative to sea level) at 5:00 AM and a low tide of -2.1m (relative to sea level) at 11:00 AM.
Based on your knowledge of tides from Earth Science, there are roughly two high tides per day,
twelve hours apart. (I recommend using Desmos to create a sinusoidal function which you can
use to answer the problems below. If you do use Desmos include a screenshot of your Desmos
screen.)

(A) What is the average height of the water over the course of a day? How much higher and
lower than the average water level is the high tide and low tide?

(B) You are expected to arrive at the Bayonne Bridge at 7:00 PM on May 3rd. Will you be able to
clear the Bayonne Bridge at that time or not? Explain why or why not.

(C) In order to plan for when you would be able to clear the Bridge, you want to find all of the
times on May 3rd, when you will be able to clear the Bridge. (You can express this in decimal
parts of the hour instead of having to convert to hours and minutes.)