Meter Stick Special Relativity Problem

[harrietstowe]

Homework Statement

A meter stick in frame S' makes an angle of 30° with the x' axis. If that frame moves parallel to the x-axis with speed 0.82c relative to frame S, what is the length of the stick as measured from S?

Homework Equations

Length contraction: L=L_o/γ

The Attempt at a Solution

Relative to s, the length of this meter stick will contract. γ=1.747
L_o = 1m
L = .572
I then multiplied this by the cosine of 30 degrees to get .088 m but this is not the right answer. Multiplying by the cosine of 30 degrees was sort of a guess as I am unsure of what to do with it.
Thanks

Thanks

 

[collinsmark]

Relative to s, the length of this meter stick will contract. γ=1.747
L_o = 1m
L = .572
I then multiplied this by the cosine of 30 degrees to get .088 m but this is not the right answer. Multiplying by the cosine of 30 degrees was sort of a guess as I am unsure of what to do with it.

Work with the x-component and y-component separately. Calculate the x-component and the y-component of the meter stick in its own frame of reference (the S' frame). Only the x-component will contract in the S frame. Then use the Pythagorean theorem to find the total length (in the S frame) after contraction.