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 I80, 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

Pythagorean Theorem

The Pythagorean theorem is applied after determining the net horizontal and vertical displacements, to compute the magnitude of the resultant vector. It provides a method to find the straight-line distance from the starting point to the ending point by treating the displacements as the legs of a right triangle.

Trigonometric Decomposition

Trigonometric decomposition involves using sine and cosine functions to split a vector into its perpendicular components when the vector is not aligned with the coordinate axes. This is crucial for resolving movements in directions like southwest, where the angle relative to the axes is known.

Vector Addition

Vector addition is the process of combining two or more vectors to determine their overall effect. In a two?dimensional space, this means adding the horizontal (x) and vertical (y) components of each vector separately to obtain the total displacement or resultant vector.

Coordinate System and Component Decomposition

Using a coordinate system allows one to break each movement or vector into its horizontal and vertical components. This is especially useful for interpreting directions such as north, east, or any other angle, as it simplifies the problem into adding numbers along the x-axis and y-axis.

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