- #1
Blanchdog
- 57
- 22
Homework Statement
Find the length of a meter stick if in the laboratory frame it is angled at 60 degrees relative to the direction of motion, and it is traveling at .8 c.
I have calculated gamma to be 1.667
Homework Equations
Lorentz transformations
The Attempt at a Solution
a' = l' cos(x), b = l' sin(x)
a = cos(60), b = sin(60)
a' = a/gamma, b' = b
l' cos(x) = cos(60)/gamma, l' sin(x) = sin(60)
combine by eliminating l'
cos(60)/(cos(x) gamma) = sin(60)/sin(x)
tan(x) = tan(60) gamma
x = arctan(tan(60) gamma)
plug x back into solve for l'
l' = cos(60)/(cos(x) gamma)
This gives me a result of about 91 cm, but the book says it should be 82 cm. Where did I go wrong?