Special Relativity (Transformation question) Check Answer.

[Lengalicious]

Homework Statement

A boat with mast at angle θ to its deck is traveling at velocity v relative to an observer, what angle does this observer see.

Homework Equations

The Attempt at a Solution

So by using Lorentz Transformation: x'=(x-vt)*g where g=gamma
The mast is length 'r'' and at an angle θ' to the deck of the moving boat, so x' = r'*cos(θ')
By substitution, r'*cos(θ') = (x-vt)g and θ' = cos^-1(x-vt/r'*√(1-(v²/c²))).

Am I right or not? Thanks

 

[Mindscrape]

Ah, yes, this is a very good problem, but only if you do the follow up of looking at the problem using velocities (that is to say a spotlight mounted to a boat forming an angle).

Anyway, to get to your answer: no, sorry it's not right. You just transformed x coordinates, but length is the difference between x coordinates. The length contraction formula is actually derived through the difference in x coordinates L'=x2'-x1'=x2*g-vt*g-x1*g+vt*g=g*(x2-x1)=g*L.