An ant is crawling along a straight wire, which we shall call the axis, from A to B to C to D (which overlaps A), as shown in the figure below. O is the origin. Suppose you take measurements and find that AB is 55.0 cm, BC is 38.0 cm, and AO is 4.00 cm Part A What is the ant's position at point A? XA Part B What is the ant's position at point B? XB = Part C VΠΙ ΑΣΦ xC = 1ΨΕΙ ΑΣΦ What is the ant's position at point C? IVE ΑΣΦ DO ? ? ? cm cm cm

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Problem Description

An ant is crawling along a straight wire, referred to as the \( x \)-axis, from point \( A \) to \( B \) to \( C \) to \( D \) (which overlaps \( A \)), as illustrated in the figure below. The point \( O \) is the origin. Measurements taken indicate that \( AB = 55.0 \, \text{cm} \), \( BC = 38.0 \, \text{cm} \), and \( AO = 4.0 \, \text{cm} \).

#### Diagram Description

The diagram shows a horizontal line representing the \( x \)-axis. Key points are marked as \( A \), \( B \), \( C \), and \( D \) along the line, with \( O \) as the origin. Distances between these points are annotated based on the given measurements.

### Part A

**Question:** What is the ant’s position at point \( A \)?

- Position \( x_A = \) \(\_\_\_\_\) cm

### Part B

**Question:** What is the ant’s position at point \( B \)?

- Position \( x_B = \) \(\_\_\_\_\) cm

### Part C

**Question:** What is the ant’s position at point \( C \)?

- Position \( x_C = \) \(\_\_\_\_\) cm

This setup requires calculating the positions based on given distances along the \( x \)-axis. The relations are as follows:
- \( x_A = AO \)
- \( x_B = x_A + AB \)
- \( x_C = x_B + BC \)

Use the provided measurements to find each position.
Transcribed Image Text:### Problem Description An ant is crawling along a straight wire, referred to as the \( x \)-axis, from point \( A \) to \( B \) to \( C \) to \( D \) (which overlaps \( A \)), as illustrated in the figure below. The point \( O \) is the origin. Measurements taken indicate that \( AB = 55.0 \, \text{cm} \), \( BC = 38.0 \, \text{cm} \), and \( AO = 4.0 \, \text{cm} \). #### Diagram Description The diagram shows a horizontal line representing the \( x \)-axis. Key points are marked as \( A \), \( B \), \( C \), and \( D \) along the line, with \( O \) as the origin. Distances between these points are annotated based on the given measurements. ### Part A **Question:** What is the ant’s position at point \( A \)? - Position \( x_A = \) \(\_\_\_\_\) cm ### Part B **Question:** What is the ant’s position at point \( B \)? - Position \( x_B = \) \(\_\_\_\_\) cm ### Part C **Question:** What is the ant’s position at point \( C \)? - Position \( x_C = \) \(\_\_\_\_\) cm This setup requires calculating the positions based on given distances along the \( x \)-axis. The relations are as follows: - \( x_A = AO \) - \( x_B = x_A + AB \) - \( x_C = x_B + BC \) Use the provided measurements to find each position.
**Part D**

What is the ant’s position at point \( D \)?

\[ x_D = \_\_\_\_\_\_\_\_ \, \text{cm} \]

*Explanation of Symbols and Interface:*

- The interface includes a mathematical input box for entering the value of \( x_D \), representing the position of the ant at point \( D \) in centimeters.
- There are options to use different mathematical notations and symbols provided by the interface, such as square roots and Greek letters, useful for complex calculations or notations.
- The icons allow for actions like undo, redo, and opening a virtual keyboard for mathematical symbols.
Transcribed Image Text:**Part D** What is the ant’s position at point \( D \)? \[ x_D = \_\_\_\_\_\_\_\_ \, \text{cm} \] *Explanation of Symbols and Interface:* - The interface includes a mathematical input box for entering the value of \( x_D \), representing the position of the ant at point \( D \) in centimeters. - There are options to use different mathematical notations and symbols provided by the interface, such as square roots and Greek letters, useful for complex calculations or notations. - The icons allow for actions like undo, redo, and opening a virtual keyboard for mathematical symbols.
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