A truck leaves a warehouse. It travels 40 kilometres south, 55 kilometres north, 5 kilometres east, 30 kilometres north, and 45 kilometres south. How far and in which direction must the truck go to get back to the warehouse?

To determine how far and in which direction the truck must travel to return to the warehouse, we need to analyze its overall displacement by summing its movements in the north-south and east-west directions separately.

### Step 1: Calculate the net displacement in the north-south direction.
- South: 40 km
- North: 55 km
- North: 30 km
- South: 45 km

Let's sum the northward and southward movements:

- Total northward movement = \( 55 + 30 = 85 \, \text{km} \)
- Total southward movement = \( 40 + 45 = 85 \, \text{km} \)

The net displacement in the north-south direction is:
\[
85 \, \text{km (north)} - 85 \, \text{km (south)} = 0 \, \text{km}
\]
So, the truck has no displacement in the north-south direction.

### Step 2: Calculate the net displacement in the east-west direction.
- East: 5 km

Since there is only an eastward movement and no westward movement, the truck is displaced 5 km to the east.

### Step 3: Determine the return direction and distance.
- The truck is now 5 km east of the warehouse.
- To return to the warehouse, the truck needs to travel 5 km west.

### Final Answer:
The truck must travel **5 kilometres west** to get back to the warehouse.

Would you like more details or have any questions?

Here are five related questions:
1. How do you calculate displacement in a 2D plane?
2. What is the difference between displacement and distance traveled?
3. How would the displacement change if the truck also moved west?
4. Can you explain how vectors work in displacement problems?
5. What would happen if the truck made a diagonal movement?

**Tip:** Displacement only considers the change in position, not the total distance traveled!

Solve a truck displacement problem involving movement in north-south and east-west directions. Learn how to calculate net displacement and determine how far the truck must go to return to the warehouse. This problem covers key mathematical concepts such as vector addition and displacement in a 2D plane, suitable for students in Grades 6-8.

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