### Problem DescriptionA brother and sister are playing in the woods. The brother realizes that they have become separated and recalls seeing his sister at a large tree. The brother initially traveled \( d_1 = 23.5 \, \text{m} \) at an angle \(\theta_1 = 22.0^\circ\) from the tree. He then turned and traveled \( d_2 = 11.0 \, \text{m} \) at \(\theta_2 = 138^\circ\).Meanwhile, the sister traveled \( d_3 = 17.0 \, \text{m} \) at an angle \(\theta_3 = 112^\circ\) from the tree. The angles are defined with respect to east, counterclockwise being defined as positive.### Task: Part B - Displacement from the Boy to the GirlUsing the method of vector addition by components, determine the displacement from the boy to the girl. #### InstructionsExpress your answers, separated by a comma, to three significant figures. Enter the angle measured counterclockwise from the positive x-axis.- **Hints Available**: Click on "View Available Hint(s)" for assistance.#### SubmissionPlease enter your computed answers in the designated input box for \( d_{BG} \) and \( \theta_{BG} \) (in meters and degrees respectively).### DiagramThe diagram illustrates paths traveled by the brother and sister with vectors originating from a common point identified as the "Tree."(Note: The diagram and figures provided are crucial for visualizing the problem and accurately applying vector addition.) **Title:** Vector Displacement in Physics**Scenario:**A brother and sister are playing in the woods, when suddenly the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree.**Brother's Path:**- **d₁ = 23.5 m** at an angle of **θ₁ = 22.0°** from the tree.- The brother then turned and traveled **d₂ = 11.0 m** at an angle of **θ₂ = 138°**.**Sister's Path:**- The sister traveled **d₃ = 17.0 m** at an angle of **θ₃ = 112°** from the tree.*Note: The angles are given with respect to east, with counterclockwise being defined as positive.***Diagram Explanation:**The figure illustrates the paths taken by the boy and the girl from the tree. The paths are represented as lines with arrows indicating direction, and the angles are measured from the east (positive x-axis), counterclockwise being positive.**Task: Displacement from the Boy to the Girl**Using the method of vector addition by components, determine the displacement from the boy to the girl.**Instructions:**1. Express your answer as \( x, y \) coordinates separated by a comma, with three significant figures.2. Enter the angle measured counterclockwise from the positive x-axis.Submit your calculated displacement values in the provided fields.

Answered: Image /qna-images/answer/2939e3d8-d243-4757-8f73-f773f4516b92.jpg

Abrother and sister are playing in the woods when suddenty the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree. The brother traveled d- 23.5m at d,- 22.0 trom the tree then turned and traveled =11.0 m at A - 138° Meanwhile, the Reviow Part B- Displacement from the boy to the girl dz Sister traveled dy = 17.0 m at an angle of O3 =-112 from the tree. The angles are given with respect to east with counterciockwise being defined as positive (Figure 1) Using the method of vector addition by components, delermine the displacement from the boy to the girl.(Eigure 3) Express your answers, separated by a comma, to three significant figures. Enter the angle measured counterclockwise from the positive x axis. > View Available Hint(s) gure 2 of 3 ΑΣφ vec dBG OBG = m, Submit

Abrother and sister are playing in the woods when suddenty the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree. The brother traveled d- 23.5m at d,- 22.0 trom the tree then turned and traveled =11.0 m at A - 138° Meanwhile, the Reviow Part B- Displacement from the boy to the girl dz Sister traveled dy = 17.0 m at an angle of O3 =-112 from the tree. The angles are given with respect to east with counterciockwise being defined as positive (Figure 1) Using the method of vector addition by components, delermine the displacement from the boy to the girl.(Eigure 3) Express your answers, separated by a comma, to three significant figures. Enter the angle measured counterclockwise from the positive x axis. > View Available Hint(s) gure 2 of 3 ΑΣφ vec dBG OBG = m, Submit

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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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Question

### Problem Description

A brother and sister are playing in the woods. The brother realizes that they have become separated and recalls seeing his sister at a large tree. The brother initially traveled \( d_1 = 23.5 \, \text{m} \) at an angle \(\theta_1 = 22.0^\circ\) from the tree. He then turned and traveled \( d_2 = 11.0 \, \text{m} \) at \(\theta_2 = 138^\circ\).

Meanwhile, the sister traveled \( d_3 = 17.0 \, \text{m} \) at an angle \(\theta_3 = 112^\circ\) from the tree. The angles are defined with respect to east, counterclockwise being defined as positive.

### Task: Part B - Displacement from the Boy to the Girl

Using the method of vector addition by components, determine the displacement from the boy to the girl.

#### Instructions

Express your answers, separated by a comma, to three significant figures. Enter the angle measured counterclockwise from the positive x-axis.

- **Hints Available**: Click on "View Available Hint(s)" for assistance.

#### Submission

Please enter your computed answers in the designated input box for \( d_{BG} \) and \( \theta_{BG} \) (in meters and degrees respectively).

### Diagram

The diagram illustrates paths traveled by the brother and sister with vectors originating from a common point identified as the "Tree."

(Note: The diagram and figures provided are crucial for visualizing the problem and accurately applying vector addition.)

**Title:** Vector Displacement in Physics

**Scenario:**
A brother and sister are playing in the woods, when suddenly the brother realizes that they are separated. The last place he remembers seeing his sister is at a particularly large tree.

**Brother's Path:**
- **d₁ = 23.5 m** at an angle of **θ₁ = 22.0°** from the tree.
- The brother then turned and traveled **d₂ = 11.0 m** at an angle of **θ₂ = 138°**.

**Sister's Path:**
- The sister traveled **d₃ = 17.0 m** at an angle of **θ₃ = 112°** from the tree.

*Note: The angles are given with respect to east, with counterclockwise being defined as positive.*

**Diagram Explanation:**
The figure illustrates the paths taken by the boy and the girl from the tree. The paths are represented as lines with arrows indicating direction, and the angles are measured from the east (positive x-axis), counterclockwise being positive.

**Task: Displacement from the Boy to the Girl**
Using the method of vector addition by components, determine the displacement from the boy to the girl.

**Instructions:**
1. Express your answer as \( x, y \) coordinates separated by a comma, with three significant figures.
2. Enter the angle measured counterclockwise from the positive x-axis.

Submit your calculated displacement values in the provided fields.

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