Final answer:
Using the length contraction formula, the dimensions of the Borg cube as observed by a stationary observer, when it passes at 0.950c, would be 85 cm in height, a contracted length which can be calculated, and 95 cm in width; only the dimension along the direction of motion contracts.
Step-by-step explanation:
The movement of the Borg cube traveling through space at high velocity is subject to the effects of length contraction as predicted by Einstein's theory of special relativity. To determine the contracted dimensions of the cube as it passes the USS Enterprise at 0.950c (95% of the speed of light), we can use the formula for length contraction:
L = L0 * √(1 - v^2/c^2)
where L is the length observed by the stationary observer, L0 is the proper length (the length of the object in the rest frame), v is the relative velocity, and c is the speed of light. Given that the cube's rest frame dimensions are height = 85 cm, length = 75 cm, and width = 95 cm, we can calculate the observed dimensions using the respective velocity for each dimension:
- Observed height = 85 cm * √(1 - (0.950c)^2/c^2)
- Observed length = 75 cm * √(1 - (0.950c)^2/c^2)
- Observed width = 95 cm * √(1 - (0.950c)^2/c^2)
However, because the cube is a three-dimensional object, the contraction only occurs along the direction of motion. Assuming the length is the dimension along the direction of motion, only this dimension will contract while the height and width remain unchanged. By calculating the contracted length, we then find the observed dimensions of the Borg cube to be 85 cm in height, a contracted length (calculated), and 95 cm in width.