According to the theory of special relativity, when an observer moves relative to an object at high velocities, length contraction occurs along the direction of motion. The formula to calculate this length contraction is given by:
L' = L * √(1 - (v^2/c^2))
Where: L' is the observed length of the meter stick by the moving observer. L is the rest length of the meter stick (1 meter in this case). v is the velocity of the observer relative to the speed of light. c is the speed of light (299,792,458 meters per second).
In this scenario, the observer is moving at one-half the velocity of light, which means v = 0.5c. Let's calculate the observed length:
L' = 1 * √(1 - (0.5c)^2) ≈ 1 * √(1 - (0.5)^2) ≈ 1 * √(1 - 0.25) ≈ 1 * √(0.75) ≈ 1 * 0.866 ≈ 0.866 meters
Therefore, the observer moving at one-half the velocity of light would measure the length of the meter stick to be approximately 0.866 meters.