• Support PF! Buy your school textbooks, materials and every day products Here!

Special Relativity (Transformation question) Check Answer.

  • #1
163
0

Homework Statement


A boat with mast at angle θ to its deck is travelling 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
 

Answers and Replies

  • #2
1,860
0
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.
 

Related Threads on Special Relativity (Transformation question) Check Answer.

Replies
3
Views
1K
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
3
Views
759
Replies
1
Views
930
Replies
1
Views
1K
Replies
5
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
14
Views
10K
Replies
3
Views
925
Replies
2
Views
898
Top