A truck travels 36 km towards the north, then turns towards the west and travels 9 km, then turns towards the south and travels 50 km, and finally turns to its left and travels 9 km. Where is the truck now with reference to its starting position?

Introduction / Context:
This question describes the path of a truck making several turns and movements in north, west, south and east directions. We are asked to find the truck's final position relative to the starting point, expressed as a direction and distance. The problem demonstrates how combining movements that partly cancel can lead to a simple net displacement even when the path itself is long.

Given Data / Assumptions:
- The truck first travels 36 km towards the north. - It then turns towards the west and travels 9 km. - It then turns towards the south and travels 50 km. - Finally it turns to its left. When facing south, a left turn points towards the east, and it travels 9 km. - We treat the starting point as the origin on a flat coordinate plane.

Concept / Approach:
We again use a coordinate approach with north as positive y, south as negative y, east as positive x and west as negative x. Movements west and east affect x, while movements north and south affect y. The key idea is that equal and opposite movements along the same axis cancel. Here, the westward and eastward legs are equal, so the net horizontal movement is zero, while the northward and southward legs differ, leaving a net southward displacement.

Step-by-Step Solution:
1. Start at (0, 0). 2. Move 36 km north: new position is (0, 36). 3. Move 9 km west: new position is (-9, 36). 4. Move 50 km south: new position is (-9, -14) because 36 - 50 = -14. 5. Facing south, turn left to face east and move 9 km: final position is (0, -14). 6. From (0, 0) to (0, -14) the displacement is 14 km towards the south.

Verification / Alternative check:
We can simplify by net sums. Total northward travel is 36 km. Total southward travel is 50 km. The net southward movement is therefore 50 - 36 = 14 km. For east west, the truck goes 9 km west and later 9 km east, which cancel out, giving net zero horizontal movement. So the truck ends directly south of the starting point at a distance of 14 km. A quick sketch shows an up, left, down, and right pattern ending directly below the origin.

Why Other Options Are Wrong:
- 14 km North reverses the correct vertical direction; the southward distance is larger. - 86 km South and 86 km North come from adding north and south distances without cancellation. - Back at the starting point would require both vertical and horizontal nets to be zero, which is not the case.

Common Pitfalls:
One frequent mistake is forgetting to change orientation correctly when turning left from south to east. Another is summing all distances and thinking that a larger total means a larger displacement. Carefully separating net movement along each axis and treating opposite directions as positive and negative avoids such errors. Drawing arrows on a simple grid is an excellent way to reinforce understanding in exam conditions.

Final Answer:
The truck is 14 km to the south of its starting point.