Why Thomas, you're all wet!

If you've ever watched sailing, you will sometimes see a sailor hanging off the side of the boat, for example in this shot from the movie "The Thomas Crown Affair." Eventually, of course, the sailboat tips over so far that a person cannot keep it balanced. Consider an idealized model of a small sailboat where the boat is a point. We'll model the mast and sails as a 14 meter long uniform rod with total mass 400 kg. Our sailor will be modeled as a 100 kg point mass on the massless boom that extends 4 meters from the boat at a right angle to the sail. If \(\theta\) is the angle between the mast and the horizontal axis, at what \(\theta\) in degrees will the sailor be unable to keep the boat upright even if he is sitting at the end of the boom?

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