There once was a ship that put to sea, and the name of that ship was...

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There once was a ship that put to sea, and the name of that ship was the Billy o' Tea. The winds blew up, her bow dipped down, and she began to cruise through incompressible (20°C) seawater at a steady rate. Consider a situation where the sail is at half mast, exposing 50 ft² of sail to the wind in a way that yields a coefficient of drag of 1.2. The weight of the ship and its cargo (mostly sugar, tea, and rum) means it is pushed into the water enough to expose 20 ft² of hull to the seawater with a coefficient of drag of 0.05. For the purposes of this problem, assume (i) the seawater is perfectly flat and calm (i.e. not moving), (ii) that the wind is always a perfect tailwind (i.e. coming from directly behind the ship, blowing over the stern of the boat and into the sail), (iii) that the only drag on the ship is pressure drag (i.e. neglect surface or "skin" drag that is not wrapped into the coefficients of drag given), and (iv) that the square footages given above are from the perspective of the fluid in question. (a) Determine the terminal velocity (mph) the Billy o' Tea could achieve (relative to the sea) if the wind was blowing at 25 mph (Sea-fact: that's about 21.7 knots!). (b) She'd not been two weeks from shore, when down on her a right whale bore. The captain called all hands and swore he'd take that whale in tow. The sail is raised to full mast, meaning its surface area has doubled to 100 ft². What is the terminal velocity (mph) of the ship now, assuming the wind speed (and the coefficient of drag of the sail) is the same? (c) For forty days or even more, the line went slack then tight once more. In this time, the usage of the ship's supplies has caused the weight of the ship to decrease, meaning it doesn't sit as low in the water. If the exposed surface area of the hull is halved to 10 ft² (with the sail still at full mast -- 100 ft²), what is the terminal velocity of the ship now (assuming the wind speed is the same)? Reminder: don't forget that, if the ship is moving, the velocity of the wind relative to the sail is not the same as the velocity of the wind relative to a stationary observer. When I'm saying the wind is blowing at 25 mph, that's relative to a stationary observer. There once was a ship that put to sea, and the name of that ship was the Billy o' Tea. The winds blew up, her bow dipped down, and she began to cruise through incompressible (20°C) seawater at a steady rate. Consider a situation where the sail is at half mast, exposing 50 ft² of sail to the wind in a way that yields a coefficient of drag of 1.2. The weight of the ship and its cargo (mostly sugar, tea, and rum) means it is pushed into the water enough to expose 20 ft² of hull to the seawater with a coefficient of drag of 0.05. For the purposes of this problem, assume (i) the seawater is perfectly flat and calm (i.e. not moving), (ii) that the wind is always a perfect tailwind (i.e. coming from directly behind the ship, blowing over the stern of the boat and into the sail), (iii) that the only drag on the ship is pressure drag (i.e. neglect surface or "skin" drag that is not wrapped into the coefficients of drag given), and (iv) that the square footages given above are from the perspective of the fluid in question. (a) Determine the terminal velocity (mph) the Billy o' Tea could achieve (relative to the sea) if the wind was blowing at 25 mph (Sea-fact: that's about 21.7 knots!). (b) She'd not been two weeks from shore, when down on her a right whale bore. The captain called all hands and swore he'd take that whale in tow. The sail is raised to full mast, meaning its surface area has doubled to 100 ft². What is the terminal velocity (mph) of the ship now, assuming the wind speed (and the coefficient of drag of the sail) is the same? (c) For forty days or even more, the line went slack then tight once more. In this time, the usage of the ship's supplies has caused the weight of the ship to decrease, meaning it doesn't sit as low in the water. If the exposed surface area of the hull is halved to 10 ft² (with the sail still at full mast -- 100 ft²), what is the terminal velocity of the ship now (assuming the wind speed is the same)? Reminder: don't forget that, if the ship is moving, the velocity of the wind relative to the sail is not the same as the velocity of the wind relative to a stationary observer. When I'm saying the wind is blowing at 25 mph, that's relative to a stationary observer.