Final answer:
Mr. Cruz's displacement is calculated using the Pythagorean theorem, since his eastward and southward movements form the legs of a right triangle. By squaring both distances, adding them, and taking the square root, his displacement is found to be 500 meters in a south-easterly direction.
Step-by-step explanation:
The subject of the question is the calculation of displacement using the Pythagorean theorem, which is a topic in mathematics. To find Mr. Cruz's displacement, we need to consider his movement as a right-angled triangle where the legs of the triangle are represented by the eastward and southward movements.
Therefore, the displacement can be calculated as follows:
- First, we recognize that Mr. Cruz's movements eastward and southward are perpendicular to each other, forming the two legs of the right triangle.
- Next, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c² = a² + b².
- Mr. Cruz drives 400 m east and 300 m south. Thus, a = 400 m and b = 300 m. Plugging these values into the formula gives us c² = (400 m)² + (300 m)².
- Calculating this, we get c² = 160,000 m² + 90,000 m² = 250,000 m².
- Finally, taking the square root of both sides to solve for c gives us the displacement, which is c = √250,000 m² = 500 m. Therefore, Mr. Cruz's displacement is 500 meters in a south-easterly direction.