Relativity and a metre stick

Question

A metre stick is observed to be only 0.9 m long to an inertial observer. At what speed, relative to the observer, must the metre stick be moving?
(a) 0.44 x10⁸ m/s
(b) 0.57 x10⁸ m/s
(c) 0.95 x10⁸ m/s
(d) 1.31 x10⁸ m/s
(e) 2.70 x10⁸ m/s

Answer:

First of all a metre stick is simply a stick 1 metre long.

The length L = 0.9 m and L_o = 1 m.

So: [L/L_o]² = 1 – v²/c² and so 0.81 = 1 – v²/c²

This gives v = 1.31x10⁸ m/s.

The correct answer is (d)