Final answer:
The magnitude of the net displacement when the explorer travels 5 m northward and 12 m westward is calculated using the Pythagorean theorem, resulting in a net displacement of 13 m in the northwest direction.
Step-by-step explanation:
To find the magnitude of the net displacement for a cave explorer who travels 5 m northward and then 12 m westward, we can use the Pythagorean theorem. This theorem allows us to calculate the hypotenuse of a right triangle when we know the lengths of the other two sides. In this case, the northward and westward displacements can be represented as the two legs of a right triangle, with the net displacement as the hypotenuse.
We calculate the net displacement using the formula:
Displacement (∞) = √(northward displacement² + westward displacement²)
Substituting the given values:
∞ = √(5 m)² + (12 m)²
∞ = √25 + 144
∞ = √169
∞ = 13 m
Therefore, the magnitude of the net displacement is 13 m NW.