Final answer:
The statement is false; objects moving at a significant fraction of the speed of light, like 50%, will undergo length contraction as per Einstein's theory of special relativity.
Step-by-step explanation:
The statement that the observed length (L) of the ship remains constant if it is traveling at 50% of the speed of light is false. When considering an object moving at a significant fraction of the speed of light, we must take into account the principles of special relativity.
According to Einstein's theory of special relativity, an object traveling at a relativistic speed (a substantial fraction of the speed of light) will experience length contraction. This effect means that the length of an object, as observed from a stationary frame, will be shorter than its length as measured in its own rest frame (the proper length).
To calculate the observed length of the ship when it is moving at a high velocity (v = 0.95c, where c is the speed of light), we can use the Lorentz contraction formula:
L = L0 √(1 - v2/c2)
If the proper length (L0) of the ship is 50 meters, the observed length L would be:
L = 50 √(1 - (0.95c)2/c2)
This calculation would yield the contracted length that appears shorter than the proper length due to relativistic effects.