A child is riding their big wheel around the neighborhood. They start by riding east for 84 meters. They turn north and ride 57 meters. They turn south and continue for 30 meters. Finally, they turn west and ride 26 meters.

What is the displacement of the child?

To find the child's displacement, we need to determine their straight-line distance from the starting point, taking into account both the horizontal (east-west) and vertical (north-south) movements.

### Horizontal movement:
- The child starts by riding **84 meters east**.
- Then they ride **26 meters west**.

Thus, the total horizontal displacement is:
\[
84 - 26 = 58 \, \text{meters east}.
\]

### Vertical movement:
- The child first rides **57 meters north**.
- Then they ride **30 meters south**.

Thus, the total vertical displacement is:
\[
57 - 30 = 27 \, \text{meters north}.
\]

### Displacement:
Now that we have the horizontal and vertical displacements, we can use the Pythagorean theorem to calculate the straight-line distance (displacement) from the starting point.

\[
\text{Displacement} = \sqrt{(58^2 + 27^2)} = \sqrt{(3364 + 729)} = \sqrt{4093} \approx 63.98 \, \text{meters}.
\]

Thus, the displacement of the child is approximately **64 meters**.

Would you like a detailed explanation of any part of the solution?

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Here are 5 questions to expand on this:

1. What is the definition of displacement in physics?
2. How is displacement different from distance traveled?
3. How would the displacement change if the child turned east again instead of west?
4. Can displacement be negative?
5. What is the significance of the Pythagorean theorem in vector calculations?

**Tip:** Always remember that displacement is a vector quantity, meaning it has both magnitude and direction!

A child is riding their big wheel around the neighborhood. They start by riding east for 84 meters. They turn north and ride 57 meters. They turn south and continue for 30 meters. Finally, they turn west and ride 26 meters. What is the displacement of the child?

Learn how to calculate the displacement of a child riding a big wheel around the neighborhood. The problem involves key concepts like displacement, vector addition, and the Pythagorean theorem. Suitable for students in Grades 6-8, this solution includes a step-by-step breakdown.

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