Question

A stick is moving along the x-axis at 90%c. A person riding with the stick sees it inclined at 45.

Answer 1

let the length of the stick be ''L''

for the person riding ::

$\theta$ = 45

so length along X-axis = L Cos45

length along Y-axis = L Sin45

since the stick moves along the X-axis , the X-component of the stick contracts which can be given as ::

L' = (L Cos45 ) sqrt(1- V²/c²)

V = 0.90c

so L' = (L Cos45 ) sqrt(1- (0.9c)²/c²)

L' = (0.43589) (L Cos45)          

angle can be given as

tan $\theta$ ' = LSin45 /L'

tan $\theta$ ' = LSin45 /(0.43589) (L Cos45)

$\theta$ ' = 66