How fast must a meter stick move, relative to the frame of the observer making the measurement, so its length will be measured to be 0.60 m?
A) 0.40c
B) 0.60c
C) 0.90c
D) 0.80c
E) 0.70c

Question

Quizplus · Accepted Answer

The length contraction formula in special relativity is given by $L = L_0\sqrt{1 - v^2/c^2}$, where $L$ is the observed length, $L_0$ is the proper length (the length of the object in its rest frame), $v$ is the relative velocity between the observer and the object, and $c$ is the speed of light. Rearranging the formula to solve for $v$, we get $v = c\sqrt{1 - (L/L_0)^2}$. Substituting $L_0 = 1$ m (the proper length of the meter stick) and $L = 0.60$ m (the observed length), we find $v = c\sqrt{1 - (0.60)^2} = c\sqrt{1 - 0.36} = c\sqrt{0.64} = 0.8c$, which corresponds to choice D.

How Fast Must a Meter Stick Move, Relative to the Frame