Length contraction of rod at angle in moving frame

[Aeighme]

Homework Statement

A rod of rest length L0 = 10.4 m moves with a speed v = 0.42c along the x axis. The rod makes an angle of q0 = 66.1° with respect to the x' axis (primed frame is moving with the rod). What is the length of the rod as measured by a stationary observer?

Homework Equations

L=L¹*(1/gamma)

The Attempt at a Solution

I have tried this several times, but can't seem to get it right.
L0=L¹=10.4
gamma=(1-.42²)^-.5
Just solved for L..but didn't work.

 

[Doc Al]

Careful. Only the component parallel to the direction of motion contracts.

 

[Aeighme]

So only the x component...is contracted. so L*cos(66.1)=L(x)?

 

[Doc Al]

So only the x component...is contracted. so L*cos(66.1)=L(x)?

Right. (That's L₀, of course.)

 

[Aeighme]

Right. (That's L₀, of course.)

now I multiply that by 1/gamma or (1-Beta²)^.5
and beta = .42...

so L=3.8238

 

[Doc Al]

now I multiply that by 1/gamma or (1-Beta²)^.5
and beta = .42...

so L=3.8238

OK so far, but realize that this is just the x-component, L_x not the full L. What's the y-component? Then calculate the measured length of the rod.