Algebraically. You may also choose to solve some of them...

Algebraically. You may also choose to solve some of them graphically to check your answers.
You first walk $8.0 \mathrm{km}$ north from home, then walk east until your displacement from home is $10.0 \mathrm{km} .$ How far east did you walk?

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Key Concepts

Vector Displacement

Displacement is a vector quantity that represents the straight-line distance from the starting point to the end point, considering both magnitude and direction. It is different from the total path traveled and is crucial in determining the actual net change in position.

Right Triangle Geometry

When movement occurs in perpendicular directions, the resulting displacement forms a right triangle. Analyzing right triangles allows one to separate movements into orthogonal components, simplifying the process of determining distances traveled in each direction.

Pythagorean Theorem

The Pythagorean theorem relates the lengths of the sides in a right triangle. It is used to calculate the unknown side when the lengths of the other two sides are known, which is essential in problems involving orthogonal displacement components.

Algebraic Problem-Solving

Algebraic methods involve setting up equations based on the known relationships, such as those from the Pythagorean theorem, and solving for unknown quantities. This systematic approach helps to derive precise solutions in a clear and logical manner.

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