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Homework Help: Problem on relativity of angles.

  1. Apr 12, 2012 #1
    1. The problem statement, all variables and given/known data

    A sailboat is manufactured so that the mast leans at an angle α with respect to the deck. An observer standing on a dock sees the boat go by at a speed v. What angle (β) does the observer say the mast makes with the deck of the boat?

    2. Relevant equations

    3. The attempt at a solution

    Say the length of the mast with respect to the boat is L. Then the horizontal and vertical projections of this length with respect to an observer on the boat are Lcosα and Lsinα respectively. According to the observer on the dock, the horizontal projection is (1/γ)Lcosα and the vertical projection is Lsinα . Thus,
    tanβ = Lsinα divided by (1/γ)Lcosα
    or, tanβ = γtanα.

    Am I not right? The answer given in the book has the angles reversed in the final answer and I am confused.
  2. jcsd
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