Chapter 29, Problem 83GP

Predict/Calculate In Conceptual Example 29-7 considered an astronaut at rest on an inclined bed inside a moving spaceship. From the point of view of observer 1, on board the ship, the astronaut has a length L₀ and is inclined at an angle θ₀ above the floor Observer 2 sees the spaceship moving to the right with a speed u.

a.    Show that the length of the astronaut as measured by observer 2 is

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

b.    (b) Show that the angle θ the astronaut makes with the floor of the ship, as measured by observer 2, is given by

     $\tan \theta =\frac{\tan {\theta }_0}{\sqrt{1-v^2/c^2}}$