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The acceleration of a rocket traveling upward is given by a = (8 + 0.028) Im/s², where s is in meters. Initially, v = 0 and s = 0 when t= 0.

The acceleration of a rocket traveling upward is given by a = (8 + 0.028) Im/s², where s is in meters. Initially, v = 0 and s = 0 when t= 0.

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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--- ### Problem Statement: The acceleration of a rocket traveling upward is given by \( a = (8 + 0.02s) \, \text{m/s}^2 \), where \( s \) is in meters. Initially, \( v = 0 \) and \( s = 0 \) when \( t = 0 \). --- #### Part A: **Question:** Determine the time needed for the rocket to reach an altitude of \( s = 170 \, \text{m} \). **Instructions:** - Express your answer to three significant figures and include the appropriate units. --- ### Diagram Explanation: The diagram provided illustrates a rocket in the process of ascending vertically with visible exhaust flames indicating propulsion. The vertical distance \( s \) from the ground to the rocket is marked to represent the altitude. --- ### Solution Steps: 1. **Understanding the Equation:** - The given acceleration \( a \) is a function of distance \( s \). - Acceleration: \( a = 8 + 0.02s \, \text{m/s}^2 \). - Initial conditions: \( v = 0 \, \text{m/s} \) and \( s = 0 \, \text{m} \) at \( t = 0 \). 2. **Finding Time \( t \):** - Integrate the equation of acceleration to find velocity and displacement. 3. **Express Answer:** - Present the final time required in proper units. --- This instructional content focuses on applying principles of kinematics to determine the time required for a rocket to reach a specific altitude. It encourages students to integrate and apply initial conditions to solve the problem accurately. ---
Transcribed Image Text:--- ### Problem Statement: The acceleration of a rocket traveling upward is given by \( a = (8 + 0.02s) \, \text{m/s}^2 \), where \( s \) is in meters. Initially, \( v = 0 \) and \( s = 0 \) when \( t = 0 \). --- #### Part A: **Question:** Determine the time needed for the rocket to reach an altitude of \( s = 170 \, \text{m} \). **Instructions:** - Express your answer to three significant figures and include the appropriate units. --- ### Diagram Explanation: The diagram provided illustrates a rocket in the process of ascending vertically with visible exhaust flames indicating propulsion. The vertical distance \( s \) from the ground to the rocket is marked to represent the altitude. --- ### Solution Steps: 1. **Understanding the Equation:** - The given acceleration \( a \) is a function of distance \( s \). - Acceleration: \( a = 8 + 0.02s \, \text{m/s}^2 \). - Initial conditions: \( v = 0 \, \text{m/s} \) and \( s = 0 \, \text{m} \) at \( t = 0 \). 2. **Finding Time \( t \):** - Integrate the equation of acceleration to find velocity and displacement. 3. **Express Answer:** - Present the final time required in proper units. --- This instructional content focuses on applying principles of kinematics to determine the time required for a rocket to reach a specific altitude. It encourages students to integrate and apply initial conditions to solve the problem accurately. ---
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