Chapter 2, Problem 38E

A plank, fixed to a sled at rest in frame S, is of length $L_0$ and makes an angle of ${\theta }_0$ with the x−axis. Later, the sled zooms through frame S at a constant speed v parallel to the x−axis. Show that according to an observer who remains at rest in frame S, the length of the plank is now

                 $L=L_0\sqrt{1-\frac{v^2}{c^2}\cos {\theta }_0}$

and the angle it makes with the x−axis is

                 $\theta ={\tan }^{-1}({\gamma }_v\tan {\theta }_0)$