Problem on relativity of angles.

[Debdutta]

Homework Statement

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?

Homework Equations

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.

 

[anathema]

Hello,

Your attempt at a solution is correct. The angle β that the observer on the dock sees the mast making with the deck of the boat is indeed given by tanβ = γtanα, where γ is the Lorentz factor.

It is possible that the answer given in the book has the angles reversed due to a typo or mistake. It is always a good idea to double check your work and the answer given in the book to make sure they match.

I hope this helps. Keep up the good work in your studies!

Scientist