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.