Part A - Position of the boy Using the parallelogram law to add these vectors geometrically, determine the displacement of the boy relative to the tree.(Figure 2) 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) ΑΣφ vec ? dp , 0B m, Submit

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Chapter1: Units, Trigonometry. And Vectors
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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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**Learning Goal:**

To be able to add and subtract vectors using geometric and vector addition.

**Problem Description:**

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. The brother traveled \( d_1 = 21.5 \, \text{m} \) at \( \theta_1 = 21.5^\circ \) from the tree then turned and traveled \( d_2 = 12.0 \, \text{m} \) at \( \theta_2 = 132^\circ \). Meanwhile, the sister traveled \( d_3 = 18.0 \, \text{m} \) at an angle of \( \theta_3 = -114^\circ \) from the tree. The angles are given with respect to east with counterclockwise being defined as positive (Figure 1).

**Task:**

**Part A - Position of the boy**

Using the parallelogram law to add these vectors geometrically, determine the displacement of the boy relative to the tree. (Figure 2)

Express your answers, separated by a comma, to three significant figures. Enter the angle measured counterclockwise from the positive x-axis.
\[ d_B, \theta_B = \]

Submit


**Figure:**

1 of 2

The image shows a diagram with vectors \(d_1\), \(d_2\), and \(d_3\) on an xy-plane. The vector \(d_1\) is positioned at an angle of \(21.5^\circ\) from the positive x-axis. The vector \(d_2\) starts from the end of \(d_1\) and is at an angle of \(132^\circ\) from the positive x-axis. The vector \(d_3\) is drawn from the tree position in the negative direction making an angle of \(-114^\circ\) from the positive x-axis.

**Further Steps:**

- Complete Part B
- Complete Part C

**Provide Feedback**
Transcribed Image Text:**Learning Goal:** To be able to add and subtract vectors using geometric and vector addition. **Problem Description:** 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. The brother traveled \( d_1 = 21.5 \, \text{m} \) at \( \theta_1 = 21.5^\circ \) from the tree then turned and traveled \( d_2 = 12.0 \, \text{m} \) at \( \theta_2 = 132^\circ \). Meanwhile, the sister traveled \( d_3 = 18.0 \, \text{m} \) at an angle of \( \theta_3 = -114^\circ \) from the tree. The angles are given with respect to east with counterclockwise being defined as positive (Figure 1). **Task:** **Part A - Position of the boy** Using the parallelogram law to add these vectors geometrically, determine the displacement of the boy relative to the tree. (Figure 2) Express your answers, separated by a comma, to three significant figures. Enter the angle measured counterclockwise from the positive x-axis. \[ d_B, \theta_B = \] Submit **Figure:** 1 of 2 The image shows a diagram with vectors \(d_1\), \(d_2\), and \(d_3\) on an xy-plane. The vector \(d_1\) is positioned at an angle of \(21.5^\circ\) from the positive x-axis. The vector \(d_2\) starts from the end of \(d_1\) and is at an angle of \(132^\circ\) from the positive x-axis. The vector \(d_3\) is drawn from the tree position in the negative direction making an angle of \(-114^\circ\) from the positive x-axis. **Further Steps:** - Complete Part B - Complete Part C **Provide Feedback**
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