According to the theory of special relativity, when an object moves at relativistic speeds (close to the speed of light), its length appears to contract from the perspective of an observer in relative motion. This phenomenon is known as length contraction.
The formula to calculate the observed length of a moving object is given by:
L' = L * √(1 - (v^2/c^2))
Where: L' is the observed length, L is the rest length (length of the stick at rest), v is the velocity of the stick relative to the observer, and c is the speed of light in a vacuum.
In this case, the stick is aligned parallel to the direction of motion, so there is no angular contraction. Assuming the rest length of the stick is 1 meter and the speed of light is approximately 3 x 10^8 meters per second (c = 3 x 10^8 m/s), we can substitute the values into the formula:
L' = 1 * √(1 - (0.8c)^2/c^2)
L' = 1 * √(1 - 0.64)
L' = 1 * √(0.36)
L' ≈ 0.6 meters
Therefore, the observed length of the stick, as measured by the observer, is approximately 0.6 meters.