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Determine the distance the ball is from the origin 3 s after being released from rest.

Determine the distance the ball is from the origin 3 s after being released from rest.

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
Problem 1.1MA
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Determine the distance the ball is from the origin 3 s after being released from rest.
Express your answer to three significant figures and include the appropriate units.
### Question The 9 lb particle is subjected to the action of its weight and forces \(\mathbf{F_1} = \{2t\mathbf{i} + 6t\mathbf{j} - 2tk\mathbf{k}\} \text{ lb}\), \(\mathbf{F_2} = \{t^2\mathbf{i} - 4t\mathbf{j} - 1k\mathbf{k}\} \text{ lb}\), and \(\mathbf{F_3} = \{-2t\mathbf{i}\} \text{ lb}\), where \(t\) is in seconds. ([Figure 1](#)) #### Part A Determine the distance the ball is from the origin 3 s after being released from rest. Express your answer to three significant figures and include the appropriate units. \[ s = \boxed{\text{Value}} \text{ ft} \] [Submit] [Previous Answers] [Request Answer] ---- ### Accompanying Information This problem involves calculating the distance of a particle from the origin after a specified time, given the forces acting on it vary with respect to time. The forces are given as vector functions of time \(t\), and it is likely that solving this problem necessitates using the principles of dynamics and kinematics. #### Explanation of Forces: - **Force \(\mathbf{F_1}\)**: A time-dependent force represented by \(\{2t\mathbf{i} + 6t\mathbf{j} - 2tk\mathbf{k}\}\) - **Force \(\mathbf{F_2}\)**: Another time-dependent force delineated by \(\{t^2\mathbf{i} - 4t\mathbf{j} - 1k\mathbf{k}\}\) - **Force \(\mathbf{F_3}\)**: The third force, with a time-dependent component, denoted \(\{-2t\mathbf{i}\}\) The task is to consider these forces and determine the resultant distance from the origin after the particle has been released from rest for a duration of 3 seconds. The problem requires integration and application of Newton’s Second Law, taking into account the mass (converted from weight), to solve for position in terms of time, and then to determine the magnitude of the positional vector at \(t = 3\) seconds. Please note, specific hints and mathematical steps
Transcribed Image Text:### Question The 9 lb particle is subjected to the action of its weight and forces \(\mathbf{F_1} = \{2t\mathbf{i} + 6t\mathbf{j} - 2tk\mathbf{k}\} \text{ lb}\), \(\mathbf{F_2} = \{t^2\mathbf{i} - 4t\mathbf{j} - 1k\mathbf{k}\} \text{ lb}\), and \(\mathbf{F_3} = \{-2t\mathbf{i}\} \text{ lb}\), where \(t\) is in seconds. ([Figure 1](#)) #### Part A Determine the distance the ball is from the origin 3 s after being released from rest. Express your answer to three significant figures and include the appropriate units. \[ s = \boxed{\text{Value}} \text{ ft} \] [Submit] [Previous Answers] [Request Answer] ---- ### Accompanying Information This problem involves calculating the distance of a particle from the origin after a specified time, given the forces acting on it vary with respect to time. The forces are given as vector functions of time \(t\), and it is likely that solving this problem necessitates using the principles of dynamics and kinematics. #### Explanation of Forces: - **Force \(\mathbf{F_1}\)**: A time-dependent force represented by \(\{2t\mathbf{i} + 6t\mathbf{j} - 2tk\mathbf{k}\}\) - **Force \(\mathbf{F_2}\)**: Another time-dependent force delineated by \(\{t^2\mathbf{i} - 4t\mathbf{j} - 1k\mathbf{k}\}\) - **Force \(\mathbf{F_3}\)**: The third force, with a time-dependent component, denoted \(\{-2t\mathbf{i}\}\) The task is to consider these forces and determine the resultant distance from the origin after the particle has been released from rest for a duration of 3 seconds. The problem requires integration and application of Newton’s Second Law, taking into account the mass (converted from weight), to solve for position in terms of time, and then to determine the magnitude of the positional vector at \(t = 3\) seconds. Please note, specific hints and mathematical steps
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