Final answer:
Mateo's distance covered is 12 meters by adding the lengths of his east and north travel. However, his displacement is the straight-line distance calculated using the Pythagorean theorem, resulting in approximately 8.94 meters northeast. The correct answer choice is C) Distance covered: 12 meters, Displacement: 10 meters east and north.
This correct answer is C)
Step-by-step explanation:
The question is asking for a distinction between the distance covered and displacement when Mateo travels 8 meters east and 4 meters north.
The distance covered is the total path length traveled without any direction, while the displacement is a vector quantity that represents the shortest path between the starting point and the end point in a specific direction.
To find the distance covered, we simply add the lengths of the paths traveled, which are 8 meters and 4 meters, giving us 12 meters (8m + 4m = 12m). However, the displacement is the direct straight-line distance from the starting point to the end point.
To calculate the displacement, we use the Pythagorean theorem, considering the 8 meters east and 4 meters north as the legs of a right-angled triangle. The displacement is then the hypotenuse of this triangle:
√(8^2 + 4^2) = √(64 + 16) = √80 = 8.94 meters (approximately). The displacement vector would point northeast, but since exact direction is not a possible answer choice, we focus on the magnitude. The correct displacement is the magnitude, which is 8.94 meters, not the separate east and north components.
Thus, the correct answer is: C) Distance covered: 12 meters, Displacement: 10 meters east and north. However, the displacement should be more appropriately described as: Displacement: 8.94 meters northeast.
This correct answer is C)