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Let's solve the problem for **Path A** step by step. Path A is represented by the green line in the grid, and each block is 120 m on a side.

### Part (a): Total Distance Traveled
We will determine the total distance traveled by counting how many blocks are traveled along the path and multiplying by the block size (120 m).

- From **Start** to **Point A**: 2 blocks east, 1 block north.
  - \(2 \times 120 = 240 \, \text{m}\) east
  - \(1 \times 120 = 120 \, \text{m}\) north

Total distance traveled = 240 m (east) + 120 m (north) = **360 m**.

### Part (b): Magnitude and Direction of Displacement
The displacement is the straight-line distance from the **Start** to **Point A**, along with the angle it makes with respect to the east direction.

1. **Magnitude of displacement** (using the Pythagorean theorem):
   - Displacement is the straight-line distance, given by:
   \[
   \text{Displacement} = \sqrt{(2 \times 120)^2 + (1 \times 120)^2}
   \]
   \[
   = \sqrt{240^2 + 120^2} = \sqrt{57600 + 14400} = \sqrt{72000} \approx 268.3 \, \text{m}
   \]

2. **Direction of displacement** (angle north of east):
   - We can calculate the angle using the tangent formula:
   \[
   \theta = \tan^{-1} \left( \frac{\text{north}}{\text{east}} \right) = \tan^{-1} \left( \frac{120}{240} \right) = \tan^{-1}(0.5)
   \]
   \[
   \theta \approx 26.57^\circ \, \text{north of east}
   \]

### Final Answer:
- (a) Total distance traveled: **360 m**
- (b) Magnitude of displacement: **268.3 m**
- Direction of displacement: **26.57° north of east**

Would you like further details or have any questions?

### 5 Related Questions:
1. How would the total distance and displacement change if Point A were farther north?
2. How do we calculate displacement for non-right-angled paths?
3. What if the blocks were not all the same size, how would this affect our method?
4. How is displacement different from total distance in real-life applications like navigation?
5. Can we use this method for 3D paths in space, and how would the formulas change?

### Tip:
When calculating displacement, remember it always refers to the shortest distance between two points, while the total distance accounts for every step taken.

Find the total distance traveled and the displacement for path A in a city grid where each block is 120 m on a side.

Learn how to calculate the total distance traveled and the magnitude of displacement for a path in a city grid, using key concepts from geometry and trigonometry. Each block is 120 meters on a side. Suitable for students in Grades 9-11.

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