A spaceship is travelling at 0.6c relative to a stationary observer and appears to be 30 m long to the stationary observer.How long is the spaceship in the spaceship's rest frame?
A)25 m
B)42 m
C)35 m
D)38 m
E)47 m

Question

Quizplus · Accepted Answer

The length of the spaceship in the spaceship's rest frame is calculated using the Lorentz contraction formula: $L = L_0 / \gamma$, where $L_0$ is the length in the rest frame, $L$ is the observed length, and $\gamma = 1/\sqrt{1 - v^2/c^2}$. However, to find $L_0$, we rearrange the formula to $L_0 = L \cdot \gamma$. Given $L = 30m$ and $v = 0.6c$, we find $\gamma = 1/\sqrt{1 - (0.6)^2} = 1.25$. Thus, $L_0 = 30m \cdot 1.25 = 37.5m$, which rounds or approximates to the closest given option.

A Spaceship Is Travelling at 0