A meter stick on a spaceship is measured in the reference frame of the Earth to have a length of 80.0 cm. The velocity of the spaceship is

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Quizplus · Accepted Answer

The length contraction formula is $L = L_0\sqrt{1 - v^2/c^2}$, where $L$ is the observed length, $L_0$ is the proper length (the length of the object in its rest frame), $v$ is the velocity of the object relative to the observer, 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 $L = 80.0$ cm (or 0.8 m) for the observed length and $L_0 = 1.0$ m for the proper length, we find $v = c\sqrt{1 - (0.8)^2} = c\sqrt{1 - 0.64} = c\sqrt{0.36} = 0.6c$.

A Meter Stick on a Spaceship Is Measured in the Reference