A farmer wants to fence off his four-sided plot of flat...

Name: Problem 22, Chapter 3: College Physics for AP® Courses
Uploaded: 2019-08-13T23:15:54-08:00
Duration: 2 min 12 s
Channel: Averell Hause
Description: A farmer wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in Figure 3.62, and then correctly calculates the length and orientation of the fourth side D . What is his result?

A farmer wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in Figure 3.62, and then correctly calculates the length and orientation of the fourth side D . What is his result?

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Key Concepts

Vector Addition in a Closed Polygon

When dealing with a closed polygon, all sides represented as vectors must add up to zero because the endpoints of the path coincide. This closure property is central to determining the unknown side since the sum of the measured sides must be balanced by the missing one.

Component Analysis of Vectors

By decomposing each side of the polygon into its horizontal and vertical components, the problem of finding the missing side reduces to solving a system of equations. This technique allows one to compute both the magnitude and the orientation of the unknown vector using the conditions that the total horizontal and vertical displacements are zero.

Graphical Methods and the Tip-to-Tail Approach

Using the tip-to-tail method provides a visual representation of vector addition where the unknown side completes the loop. This graphical understanding reinforces the concept that the final side must ‘return’ to the starting point, thus striking a balance with the other measured sides.

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