The length of a spaceship is measured to be exactly one-third its length at rest. The speed of the spaceship relative to the ground observer is:

Correct option is B

​$$\begin{aligned}&\text{Given:} \\&\bullet \ \text{Contracted length observed } L' = \frac{1}{3}L \\&\bullet \ L \text{ is the rest length of the spaceship} \\&\bullet \ \text{Need to find speed } v \text{ of the spaceship as a fraction of } c \\[10pt]&\text{Length contraction formula in special relativity:} \\&L' = L \sqrt{1 - \frac{v^2}{c^2}} \\[10pt]&\frac{L'}{L} = \sqrt{1 - \frac{v^2}{c^2}} \\[10pt]&\text{Squaring both sides:} \\&\left( \frac{L'}{L} \right)^2 = 1 - \frac{v^2}{c^2} \Rightarrow \frac{v^2}{c^2} = 1 - \left( \frac{1}{3} \right)^2 = 1 - \frac{1}{9} = \frac{8}{9} \\[10pt]&\frac{v}{c} = \sqrt{\frac{8}{9}} = 0.943\end{aligned}$$​​