The Bonneville Salt Flats, located in Utah near the border...

The Bonneville Salt Flats, located in Utah near the border with Nevada, not far from interstate $I-80$, cover an area of over 30,000 acres. A race car driver on the Flats first heads north for $4.47 \mathrm{~km}$, then makes a sharp turn and heads southwest for $2.49 \mathrm{~km},$ then makes another turn and heads east for $3.59 \mathrm{~km} .$ How far is she from where she started?

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Key Concepts

Vector Addition

This concept involves combining several vectors—each with both a magnitude and direction—to determine a single resultant vector. In navigation and displacement problems, each segment of a journey is represented as a vector. The overall effect or net displacement is then found by adding these vectors together, which often involves breaking them into components and summing the corresponding horizontal and vertical parts.

Coordinate System

A coordinate system provides a framework for analyzing directions and distances by assigning numerical values to positions in space. When dealing with problems involving movement in specific directions, such as north, east, or any other orientation, a coordinate system (typically with axes representing directions such as east-west and north-south) facilitates the calculation of vector components and the subsequent use of mathematical tools to find distances.

Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. When a displacement problem is reduced to finding the distance between two points—after determining the horizontal and vertical components of the net movement—the theorem is used to compute the distance by taking the square root of the sum of the squares of these components.

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