If a person drives a car 40.0 km [N] from X to Y and then 30.0 km [W] from Y to Z, what isthe displacement of the original position from the final position?

To solve this problem, we can use the Pythagorean theorem because the movement forms a right triangle. The displacement is the hypotenuse of the triangle.

Step 1: Identify the given distances. The person drives 40.0 km north and then 30.0 km west.

Step 2: Apply the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, a = 40.0 km and b = 30.0 km.

So, c² = a² + b² c² = (40.0 km)² + (30.0 km)² c² = 1600 km² + 900 km² c² = 2500 km²

Step 3: Solve for c (the displacement) by taking the square root of both sides.

c = √2500 km² c = 50.0 km

So, the displacement from the original position (X) to the final position (Z) is 50.0 km.