### Fundamental Problem 12.47**Problem Statement:**The boats \( A \) and \( B \) travel with constant speeds of \( v_A = 18 \, \text{m/s} \) and \( v_B = 11 \, \text{m/s} \) when they leave the pier at \( O \) at the same time. ([Figure 1](#))**Figure Explanation:**In Figure 1, two boats, labeled \( A \) and \( B \), are shown departing from a common point O at the pier. - **Boat A:** Travels in a direction that forms an angle of 60° with the horizontal axis.- **Boat B:** Travels in a direction that forms an angle of 30° with the horizontal axis.The diagram includes:1. The pier at point \( O \).2. Two boat trajectories indicated by vectors labeled with \( v_A \) and \( v_B \).3. The angles: - \( v_A \) makes a 60° angle with the horizontal direction. - \( v_B \) makes a 30° angle with the horizontal direction. The distance between each boat and the pier increases over time as they travel with their respective constant speeds.---#### Analysis:Using trigonometry and vector analysis, one can find various parameters like the distance between the boats after a certain time, the relative velocity of one boat with respect to the other, and other kinematic properties. This setup is relevant for understanding relative motion in two dimensions and applying basic principles of trigonometry and vector decomposition in physics. ### Educational Website Transcription---**Part A: Distance Calculation****Objective:**Determine the distance between two objects at the time \( t = 4 \) seconds.**Instructions:**- Express your answer to three significant figures.- Ensure to include the appropriate units.**Input:**\[ d_{AB} = \]- **Value**: [ Input Field for Numerical Value ]- **Units**: [ Input Field for Units ]**Buttons and Options:**- **Micro symbol (µ button)**: For inserting special characters.- **Undo arrow**: To undo the last action.- **Redo arrow**: To redo the last action.- **Keyboard icon**: To display an on-screen keyboard.- **Question mark (?)**: For help or additional information.**Submit and Request Answer:**- **Submit**: To submit the answer.- **Request Answer**: To request the correct answer if needed.**Feedback:**- **Provide Feedback**: A link to provide feedback on the question.---This section allows students to calculate and input the distance between two objects at a specific time \( t = 4 \) seconds, ensuring that their answer is given with three significant figures and appropriate units. The interface includes helpful buttons for character input, undo/redo actions, an on-screen keyboard, and access to help. Students can submit their answer for evaluation or request the correct answer if necessary. The feedback link provides a way for students to share their thoughts on the question.

Introduction: An object's motion is defined as the change in its position with regard to time, but…

Answered: The boats A and B travel with constant…

The boats A and B travel with constant speeds of A = 18 m/s and VB = 11 m/s when they leave the pier at O at the same time. (Figure UB

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

### Fundamental Problem 12.47

**Problem Statement:**

The boats \( A \) and \( B \) travel with constant speeds of \( v_A = 18 \, \text{m/s} \) and \( v_B = 11 \, \text{m/s} \) when they leave the pier at \( O \) at the same time. ([Figure 1](#))

**Figure Explanation:**

In Figure 1, two boats, labeled \( A \) and \( B \), are shown departing from a common point O at the pier.
- **Boat A:** Travels in a direction that forms an angle of 60° with the horizontal axis.
- **Boat B:** Travels in a direction that forms an angle of 30° with the horizontal axis.

The diagram includes:
1. The pier at point \( O \).
2. Two boat trajectories indicated by vectors labeled with \( v_A \) and \( v_B \).
3. The angles:
- \( v_A \) makes a 60° angle with the horizontal direction.
- \( v_B \) makes a 30° angle with the horizontal direction.

The distance between each boat and the pier increases over time as they travel with their respective constant speeds.

---

#### Analysis:
Using trigonometry and vector analysis, one can find various parameters like the distance between the boats after a certain time, the relative velocity of one boat with respect to the other, and other kinematic properties.

This setup is relevant for understanding relative motion in two dimensions and applying basic principles of trigonometry and vector decomposition in physics.

### Educational Website Transcription

---

**Part A: Distance Calculation**

**Objective:**
Determine the distance between two objects at the time \( t = 4 \) seconds.

**Instructions:**
- Express your answer to three significant figures.
- Ensure to include the appropriate units.

**Input:**
\[ d_{AB} = \]

- **Value**: [ Input Field for Numerical Value ]
- **Units**: [ Input Field for Units ]

**Buttons and Options:**
- **Micro symbol (µ button)**: For inserting special characters.
- **Undo arrow**: To undo the last action.
- **Redo arrow**: To redo the last action.
- **Keyboard icon**: To display an on-screen keyboard.
- **Question mark (?)**: For help or additional information.

**Submit and Request Answer:**
- **Submit**: To submit the answer.
- **Request Answer**: To request the correct answer if needed.

**Feedback:**
- **Provide Feedback**: A link to provide feedback on the question.

---

This section allows students to calculate and input the distance between two objects at a specific time \( t = 4 \) seconds, ensuring that their answer is given with three significant figures and appropriate units. The interface includes helpful buttons for character input, undo/redo actions, an on-screen keyboard, and access to help. Students can submit their answer for evaluation or request the correct answer if necessary. The feedback link provides a way for students to share their thoughts on the question.

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