In an inertial frame a rod of proper length L is at rest and at an angle θ with respect to the x-axis with relativistic speed relative to
(a) Show that the product tan θ. Lx is independent of which frame it is evaluated in:
tanθ.Lx = tanθ'. Lx'
where Lx and Lx' are the projections of the rod length onto the x-axis in frames and , respectively.
(b) In frame the rod is at an angle θ = 30◦ knowing that an observer in frame measures the rod to be at an angle θ' = 45◦ with respect to the x-axis, determine the speed at which the rod is moving with respect to the observer.
