A child is riding their big wheel around the neighborhood. They start by riding east for 97 meters. They turn north and ride 57 meters. They turn south and continue for 10 meters. Finally, they turn west and ride 10 meters.

What is the displacement of the child?

To find the displacement of the child, we need to determine the straight-line distance between the starting point and the final position. Displacement is a vector quantity, meaning it has both magnitude and direction.

### Step 1: Determine the net movement in the east-west direction
- The child first rides **east** for 97 meters.
- Finally, the child rides **west** for 10 meters.

Net movement in the east-west direction:
\[
97 \text{ meters (east)} - 10 \text{ meters (west)} = 87 \text{ meters (east)}
\]

### Step 2: Determine the net movement in the north-south direction
- The child rides **north** for 57 meters.
- Then, the child rides **south** for 10 meters.

Net movement in the north-south direction:
\[
57 \text{ meters (north)} - 10 \text{ meters (south)} = 47 \text{ meters (north)}
\]

### Step 3: Calculate the magnitude of the displacement
The displacement can be found using the Pythagorean theorem since the movements form a right triangle:
\[
\text{Displacement} = \sqrt{(87 \text{ meters})^2 + (47 \text{ meters})^2}
\]

Calculating the squares:
\[
87^2 = 7569, \quad 47^2 = 2209
\]

Adding them together:
\[
\sqrt{7569 + 2209} = \sqrt{9778} \approx 98.89 \text{ meters}
\]

### Final Answer:
The magnitude of the child's displacement is approximately **98.89 meters** in a direction northeast.

Would you like more details on how to calculate the direction of this displacement or any other aspect of this problem?

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**Related Questions:**
1. How do you determine the direction of a vector?
2. What is the difference between distance and displacement?
3. How would the displacement change if the child moved further west at the end?
4. How do you calculate the displacement if the child had returned to the starting point?
5. How would you represent this scenario graphically?

**Tip:** Displacement always refers to the shortest path between the initial and final positions, regardless of the path taken.

A child is riding their big wheel around the neighborhood. They start by riding east for 97 meters. They turn north and ride 57 meters. They turn south and continue for 10 meters. Finally, they turn west and ride 10 meters. What is the displacement of the child?

Learn how to calculate the displacement of a child's movement using vector addition and the Pythagorean theorem. The problem involves determining the straight-line distance after movements in different directions. Suitable for students in Grades 6-8.

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