A meter stick is observed to be only 0.850 meters long to an inertial observer. At what speed, relative to the observer, must the meter stick be moving?

Question

Quizplus · Accepted Answer

We can use the Lorentz contraction formula:
L' = L/sqrt(1-v^2/c^2)
where L = 1 m (the rest length of the meter stick), L' = 0.850 m (the observed length), c = 3.00 x 10^8 m/s (the speed of light), and we are solving for v (the velocity of the meter stick).
Plugging in the values, we get:
0.850 m = 1 m / sqrt(1 - v^2/c^2)
Simplifying and rearranging, we get:
v^2/c^2 = 1 - (0.850 m/1 m)^2 = 0.28
v = c * sqrt(0.28) = 1.58 x 10^8 m/s
Therefore, the answer is B.

A Meter Stick Is Observed to Be Only 0