A child walks 5.0 meters north, then 4.0 meters east, and...

A child walks $5.0$ meters north, then $4.0$ meters east, and finally $2.0$ meters south. What is the magnitude of the resultant displacement of the child after the entire walk?
(A) $1.0 \mathrm{~m}$
(B) $5.0 \mathrm{~m}$
(C) $3.0 \mathrm{~m}$
(D) $11.0 \mathrm{~m}$

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Key Concepts

Resultant Displacement

Resultant displacement refers to the overall change in position achieved after combining all individual displacements. Unlike total distance, which sums all traveled distances, resultant displacement provides the shortest path between the starting and ending points.

Pythagorean Theorem

The Pythagorean theorem is a mathematical principle used to calculate the magnitude of a resultant displacement when the displacement vectors form a right triangle. By squaring the perpendicular components, summing them, and taking the square root, one obtains the magnitude of the net displacement.

Vector Addition

Vector addition is the process of combining two or more vectors to form a resultant vector. This method involves adding corresponding components (for example, north-south and east-west directions) of each vector to determine the total effect or net displacement.

Coordinate System

A coordinate system, such as the Cartesian plane with defined axes (e.g., north-south and east-west), provides a framework to assign directions and signs to displacement vectors. It allows the separation of movements into perpendicular components, facilitating easier computation of resultant quantities.

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