Rod moving at relativistic speed: length contraction and rotation

[adamaero]

Homework Statement

A rod of length L0 moves with a speed v along the horizontal direction. The rod makes an angle of θ₀ with respect to the x'-axis.
(a) Show that the length of the rod as measured by a stationary observer is given by
L = L₀*√[1-(v²/c²)cos²θ₀]

(b) Show that the angle that the rod makes with the x-axis is given by the expression
tanθ = γ*tanθ₀

These results show that the rod is both contracted and rotated. (Take the lower end of the rod to be at the origin of the primed coordinate system.)

Homework Equations

Length Contraction
https://wikimedia.org/api/rest_v1/media/math/render/svg/c6791c2cda6e3f705aabf1345447c0864e250f38

Pythagorean Thm

sin²x + cos²x = 1

Trig ~ tanθ = opp./adj.

The Attempt at a Solution

I realize now that a mix was needed magic bag of math tricks. The picture alone...
But, honestly, I just looked it up:
http://web.unbc.ca/~hussein/Phys_205_Fall_2004/temp/Phys_205_Ch01.pdf#page=4
Static or Physics I, where were you?
Note to self, look at the general structure of the final equation. (Forget about the Einstein equations for a moment.)
In sum, this problem required deeper understanding of past concepts. It is about the knowledge foundation. A roman room may suffice...but that simple identity would have been lost in einstellung anyway? Is it worth it? I didn't learn it deeply in the first place. ADD is inconvenient.

 

[Simon Bridge]

You could use the lorentz transformation on the coordinates for the endpoints of the rod.

It is about the knowledge foundation. A roman room may suffice...but that simple identity would have been lost in einstellung anyway? Is it worth it? I didn't learn it deeply in the first place. ADD is inconvenient.

... these questions do not make sense.