Final answer:
The total distance traveled by the explorer is 31 km, and the displacement is approximately 19.3 km towards the northeast. Displacement considers both magnitude and direction, unlike distance which is a scalar quantity.
Step-by-step explanation:
The student has asked about the total distance and displacement traveled by an explorer who moves 10 km due east, then 18 km north, and finally 3 km west. To solve this, we can analyze the movement in two parts: calculating the total distance and finding the resultant displacement using vector addition.
The total distance is simply the sum of all distances traveled in any direction. This will be:
10 km (east) + 18 km (north) + 3 km (west) = 31 km.
To calculate the displacement, which is a vector quantity, we need to consider the direction and magnitude. We can represent the east and west movements along the horizontal axis and the north movement along the vertical axis. The explorer finishes 10-3=7 km east and 18 km north from the starting point. Using the Pythagorean theorem, the magnitude of the displacement is √(7² + 18²) km, which simplifies to √(49 + 324) km, or √373 km, approximately 19.3 km. The direction of the displacement can be found using trigonometry, particularly the tangent function, to calculate the angle of displacement from the eastward direction.