Question

A.An observer moving at a speed of 0.810 c relative to a rod measures its length to be 2.00 m and sees its length to be oriented at 30.0 degrees with respect to the direction of motion. What is the proper length of the rod?

B.What is the orientation angle in a reference frame moving with the rod?

Please help I know length contraction formula is involved but I keep getting an incorrect answer of 2.95 m. I have no idea on part B

Answer 1

Lx' = 1/gamma Lx

Ly' = Ly

It is given that

Lx' = 1/2 sqrt(3) * 2 m = sqrt(3) m

This means that

Lx = gamma sqrt(3) m = 2.95 m

Ly' = 1/2 * 2 m = 1 m

So, we have:

Ly = Ly' = 1 m

The proper length is thus:

L = sqrt(Lx^2 + Ly^2) = 3.12 m