A car is driven 125.0 km due west, then 65.0 km due south. What is the magnitude of its displace

step 1 The car has moved 125 km due west and 65 km due south. So the displacement of the car is in this

A car is driven 125.0 km due west, then 65.0 km due south....

A car is driven $125.0 \mathrm{km}$ due west, then $65.0 \mathrm{km}$ due south. What is the magnitude of its displacement? Solve this problem both graphically and mathematically, and check your answers against each other.

Key Concepts

Graphical Method

The graphical method involves drawing vectors to scale and positioning them head-to-tail to visually represent their addition. This method aids in understanding the physical behavior of vectors and in approximating the magnitude and direction of the resultant vector.

Mathematical Method

The mathematical method uses algebraic formulas to compute vector quantities precisely. By decomposing vectors into their components and employing equations like the Pythagorean theorem, one can accurately calculate the magnitude of the resultant displacement.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. In vector problems where movements occur at right angles, it is used to calculate the magnitude of the resultant vector by treating the individual displacements as perpendicular components.

Displacement

Displacement is a vector quantity that represents the overall change in position of an object. Unlike distance, displacement has both magnitude and direction, and is determined by the straight-line path between the starting and ending points.

Vector Addition

Vector addition involves combining vectors to produce a resultant vector, representing the net effect of multiple individual movements or forces. This concept is crucial in physics to determine quantities such as displacement or net force, and can be performed both algebraically and graphically.

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