According to the theory of special relativity, the measured speed of an object moving at relativistic speeds is not simply the sum of velocities as it is in classical mechanics. Instead, relativistic velocity addition must be used to calculate the measured speed.
The relativistic velocity addition formula is given by:
v' = (v1 + v2) / (1 + (v1 * v2 / c^2))
Where: v' is the measured velocity of the object v1 is the velocity of the object relative to the observer (Earth in this case) v2 is the velocity of the observer (in this case, the speed of light, which is approximately 3 x 10^8 m/s) c is the speed of light in a vacuum
Let's plug in the values:
v1 = 0.5c (half the speed of light) v2 = c (speed of light)
v' = (0.5c + c) / (1 + (0.5c * c / c^2)) = (1.5c) / (1 + 0.5) = (1.5c) / 1.5 = c
Therefore, the measured speed of an object traveling at half the speed of light relative to Earth is equal to the speed of light itself. In this case, the measured speed is not 0.33 times the speed of light but rather equal to the speed of light, as predicted by special relativity.