Final answer:
The westward displacement of the train can be calculated using the Pythagorean theorem, and it is found to be approximately 265 km. This is after being displaced 213 km to the south from an initial 478 km straight stretch.
Step-by-step explanation:
The student's question involves determining the train's displacement to the west, given that it first travels 478 km along a straight stretch and is then displaced 213 km south. To find the westward displacement, we need to apply the Pythagorean theorem to the given displacements, assuming the train initially traveled eastward before it was displaced southward.
Using the formula c2 = a2 + b2, where c is the hypotenuse (i.e., the 478 km stretch) and a and b are the other two sides (with a being the southward displacement of 213 km), we can solve for b (the displacement to the west).
So, b2 = c2 - a2 will give us: b2 = 4782 - 2132. Calculating this, we find that b is approximately 265 km. Therefore, the correct displacement to the west is 265 km, which corresponds to option A).