QCAA Physics Special relativity

This calculation incorrectly treats the given 125 m as the proper length ($L_0$) and solves for the contracted length. Since the observer on the spaceship is at rest relative to it, they measure the proper length, which must be longer than the contracted length measured by the outside observer.

The observer on board measures the proper length ($L_0$). Using the length contraction formula $L = L_0 \sqrt{1 - \frac{v^2}{c^2}}$, with $L=125$ m and $v=0.3c$, we rearrange to find $L_0 = \frac{125}{\sqrt{1 - 0.09}} \approx 131$ m.

This answer results from omitting the square root in the Lorentz factor calculation, dividing 125 by $(1 - 0.3^2)$ instead of $\sqrt{1 - 0.3^2}$.

This value is incorrect and does not align with the standard length contraction formula. It likely results from a calculation error or misapplication of the Lorentz factor $\gamma$.

Proper length ($L_0$) is defined as the length of an object measured in the inertial reference frame in which the object is at rest.

If the object is in motion relative to the reference frame, the measured length is the contracted length ($L$), which is shorter than the proper length due to length contraction.

Proper length is defined by the object's state of rest relative to the observer, not by acceleration.

Even if the motion is constant (not accelerating), measuring an object moving relative to the frame results in length contraction, not proper length.