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A model rocket is launched from point A with an initial velocity vo of 84 m/s. Also, the rocket's descent parachute does not deploy and the rocket lands a distance d = 100 m from A. 30° d = 100 m Determine the angle a that vo forms with the vertical. (You must provide an answer before moving on to the next part.) The angle a that vo forms with the vertical is

A model rocket is launched from point A with an initial velocity vo of 84 m/s. Also, the rocket's descent parachute does not deploy and the rocket lands a distance d = 100 m from A. 30° d = 100 m Determine the angle a that vo forms with the vertical. (You must provide an answer before moving on to the next part.) The angle a that vo forms with the vertical is

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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### Educational Resource on Rocket Trajectory --- #### Rocket Launch Problem **Problem Description:** A model rocket is launched from point \( A \) with an initial velocity \( v_0 \) of 84 m/s. The rocket's descent parachute does not deploy and it lands a distance \( d \) of 100 m from point \( A \). **Illustration Explanation:** The provided diagram shows the trajectory of a model rocket after being launched. The rocket's path forms a parabolic arc due to the influence of gravity. Here are the key elements: 1. **Point A:** This is the launch point of the rocket. 2. **Initial Velocity (\( v_0 \)):** The rocket is launched upwards and to the right from point A with an initial velocity of 84 m/s following an angle \(\alpha\) with respect to the vertical. 3. **Angle \( \alpha \):** This is the angle between the initial velocity vector (\( v_0 \)) and the vertical. 4. **Distance \( d \):** The horizontal distance from point A to the landing point B is 100 m. 5. **Launch Angle:** The diagram indicates a 30° launch inclination with the horizontal. Considering these elements helps in setting up the problem and understanding how to resolve for \(\alpha\). **Task:** Determine the angle \( \alpha \) that the initial velocity \( v_0 \) forms with the vertical axis. --- **Given Data:** - \(v_0 = 84 \, \text{m/s}\) - \(d = 100 \, \text{m}\) **Solution:** Using basic principles of projectile motion, you can solve for the angle \(\alpha\) with appropriate kinematic equations. You need to decompose the motion into horizontal and vertical components and use trigonometric relationships to find \(\alpha\). **Required Calculation:** Before moving on, you need to solve for \(\alpha\). **Answer Box:** The angle \(\alpha\) that \( v_0 \) forms with the vertical is ______°. --- By analyzing and solving this problem, you will enhance your understanding of projectile motion principles and how to apply them to real-world scenarios.
Transcribed Image Text:### Educational Resource on Rocket Trajectory --- #### Rocket Launch Problem **Problem Description:** A model rocket is launched from point \( A \) with an initial velocity \( v_0 \) of 84 m/s. The rocket's descent parachute does not deploy and it lands a distance \( d \) of 100 m from point \( A \). **Illustration Explanation:** The provided diagram shows the trajectory of a model rocket after being launched. The rocket's path forms a parabolic arc due to the influence of gravity. Here are the key elements: 1. **Point A:** This is the launch point of the rocket. 2. **Initial Velocity (\( v_0 \)):** The rocket is launched upwards and to the right from point A with an initial velocity of 84 m/s following an angle \(\alpha\) with respect to the vertical. 3. **Angle \( \alpha \):** This is the angle between the initial velocity vector (\( v_0 \)) and the vertical. 4. **Distance \( d \):** The horizontal distance from point A to the landing point B is 100 m. 5. **Launch Angle:** The diagram indicates a 30° launch inclination with the horizontal. Considering these elements helps in setting up the problem and understanding how to resolve for \(\alpha\). **Task:** Determine the angle \( \alpha \) that the initial velocity \( v_0 \) forms with the vertical axis. --- **Given Data:** - \(v_0 = 84 \, \text{m/s}\) - \(d = 100 \, \text{m}\) **Solution:** Using basic principles of projectile motion, you can solve for the angle \(\alpha\) with appropriate kinematic equations. You need to decompose the motion into horizontal and vertical components and use trigonometric relationships to find \(\alpha\). **Required Calculation:** Before moving on, you need to solve for \(\alpha\). **Answer Box:** The angle \(\alpha\) that \( v_0 \) forms with the vertical is ______°. --- By analyzing and solving this problem, you will enhance your understanding of projectile motion principles and how to apply them to real-world scenarios.
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### Projectile Motion Problem A model rocket is launched from point \(A\) with an initial velocity \(v_0\) of 84 m/s. Also, the rocket’s descent parachute does not deploy and the rocket lands a distance \(d = 100\) m from \(A\). ![Rocket Launch Diagram](diagram.png) In the given diagram: - Point \(A\) represents the launch position. - The rocket is initially launched at an unknown angle \(\alpha\) with the vertical. - The rocket travels in a parabolic trajectory and lands at point \(B\) which is 100 meters horizontally from point \(A\). - The launch path forms a 30-degree angle with the horizontal ground. - The initial velocity vector \(v_0\) is shown pointing upwards and to the right at angle \(\alpha\) from the vertical. - A blue parabolic trajectory indicates the rocket’s flight path. ### Problem Statement **Determine the angle \(\alpha\) that \(v_0\) forms with the vertical.** (Note: You must provide an answer before moving on to the next part.) Given answer: The angle \(\alpha\) that \(v_0\) forms with the vertical is \(3.457^\circ\). ❌ (Incorrect) ### Explanation of Diagrams - **Initial Velocity Vector (\(v_0\))**: This arrow represents the speed and direction at which the rocket is launched. It forms an angle \(\alpha\) with the vertical axis. - **Trajectory Path**: The path followed by the rocket as it moves upwards and then back down, shaped as a parabola due to the influence of gravity. - **Horizontal Distance (\(d\))**: The horizontal distance from the launch point \(A\) to the landing point \(B\), given as 100 meters. - **Angle with Horizontal (\(30^\circ\))**: The launch plane makes an angle of 30 degrees with the horizontal ground. This problem involves solving for the launch angle \(\alpha\) using the given distances and angles.
Transcribed Image Text:### Projectile Motion Problem A model rocket is launched from point \(A\) with an initial velocity \(v_0\) of 84 m/s. Also, the rocket’s descent parachute does not deploy and the rocket lands a distance \(d = 100\) m from \(A\). ![Rocket Launch Diagram](diagram.png) In the given diagram: - Point \(A\) represents the launch position. - The rocket is initially launched at an unknown angle \(\alpha\) with the vertical. - The rocket travels in a parabolic trajectory and lands at point \(B\) which is 100 meters horizontally from point \(A\). - The launch path forms a 30-degree angle with the horizontal ground. - The initial velocity vector \(v_0\) is shown pointing upwards and to the right at angle \(\alpha\) from the vertical. - A blue parabolic trajectory indicates the rocket’s flight path. ### Problem Statement **Determine the angle \(\alpha\) that \(v_0\) forms with the vertical.** (Note: You must provide an answer before moving on to the next part.) Given answer: The angle \(\alpha\) that \(v_0\) forms with the vertical is \(3.457^\circ\). ❌ (Incorrect) ### Explanation of Diagrams - **Initial Velocity Vector (\(v_0\))**: This arrow represents the speed and direction at which the rocket is launched. It forms an angle \(\alpha\) with the vertical axis. - **Trajectory Path**: The path followed by the rocket as it moves upwards and then back down, shaped as a parabola due to the influence of gravity. - **Horizontal Distance (\(d\))**: The horizontal distance from the launch point \(A\) to the landing point \(B\), given as 100 meters. - **Angle with Horizontal (\(30^\circ\))**: The launch plane makes an angle of 30 degrees with the horizontal ground. This problem involves solving for the launch angle \(\alpha\) using the given distances and angles.
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