Final answer:
The car traveled a total distance of 84 km and ended up 4 km west and 22 km north from its starting point. The total distance the car traveled is 84 km, and the displacement is approximately 11.31 km at a 45-degree angle to the north of east.
Step-by-step explanation:
To find the total distance traveled by the car, we add up the distances traveled in each direction:
12 km east
22 km north
6 km south
To do this, we can represent each direction as a vector and add them up. For example, the displacement of traveling 12 km east can be represented as (12, 0) and the displacement of traveling 8 km south can be represented as (0, -8).
Adding up all the vectors gives us a final displacement of (-4, 22) km. This means that the car ended up 4 km west and 22 km north from its starting point.
The total distance the car traveled is 84 km, and the displacement is approximately 11.31 km at a 45-degree angle to the north of east.
To find the total distance and displacement that the car traveled, we need to consider each segment of the trip separately. The car travels in a sequence of directional movements: 12 km east, 8 km south, 20 km west, 22 km north, 16 km east, and finally 6 km south.
To calculate the total distance, we simply add up all the lengths of the trips regardless of direction:
12 km east + 8 km south + 20 km west + 22 km north + 16 km east + 6 km south = 84 km
To find the displacement, we need to consider the net movement in the east-west direction and the north-south direction:
East-west displacement: 12 km east + 20 km west + 16 km east = 8 km east
North-south displacement: 22 km north + 8 km south - 6 km south = 8 km north
We then use the Pythagorean theorem to find the magnitude of the displacement:
√(8² + 8²) km = √(64 + 64) km = √128 km ≈ 11.31 km
The direction of the displacement can be determined by calculating the angle using trigonometry (tangent function), but since the east-west and north-south displacements are equal, the angle is 45 degrees to the north of east.