In a mood for some physics as you look at a sailboat on a lake, you wonder about its stability when a strong wind blows from the side. The sailboat leans over in the wind and the question is whether its keel can prevent it from being blown over completely.
Analyze the stability of the sailboat using the following oversimplified model.
Consider the hull of the sailboat as an airtight hollow cylinder. On top of this cylinder and perpendicular to it sits a mast carrying a square sail, assumed to be always parallel to the length of the hull. Attached to the bottom of the hull is a keel in the shape of a square always parallel to the sail. A heavy lead weight forms the bottom of the keel under water. Other than the lead weight, consider mast, sail, hull, and keel to be weightless. Somewhat unrealistically (it would make tacking difficult), you can also assume that the sail extends all the way from the bottom to the top of the mast.
(a) Establish a relationship between wind speed and the angle θ the mast will tilt away from its initial upright position when a wind with speed vw blows perpendicular (initially) to the sail.