Q24. The buoyancy force on the 580-kg balloon is F = 6 kN, and the air force acting on the balloon is Fair = {C₁.ti-C₂. √tj} N. when this time in seconds, constants C₁ = 24 and C₂ = 240. If the balloon starts from rest, determine its speed after 28 seconds. Neglect the size of the balloon but don't neglect its weight. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper Sl unit. Take g = 9.81 m/s².
Q24. The buoyancy force on the 580-kg balloon is F = 6 kN, and the air force acting on the balloon is Fair = {C₁.ti-C₂. √tj} N. when this time in seconds, constants C₁ = 24 and C₂ = 240. If the balloon starts from rest, determine its speed after 28 seconds. Neglect the size of the balloon but don't neglect its weight. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper Sl unit. Take g = 9.81 m/s².
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 24: Buoyancy and Air Force on a Balloon**
A 580-kg balloon experiences a buoyancy force \( F = 6 \, \text{kN} \). The air force acting on the balloon is defined by the equation:
\[
F_{\text{air}} = \{ C_1 \cdot t \, i - C_2 \cdot \sqrt{t} \, j \} \, \text{N}
\]
where \( t \) is time in seconds, and the constants are \( C_1 = 24 \) and \( C_2 = 240 \).
**Task:** If the balloon starts from rest, determine its speed after 28 seconds. Neglect the size of the balloon but do not neglect its weight. Ensure your answer includes two decimal places and uses proper SI units. Assume \( g = 9.81 \, \text{m/s}^2 \).
**Diagram Explanation:**
- The diagram shows a hot air balloon with upward buoyancy force \( F = 6 \, \text{kN} \).
- Axis system is shown with \( x \) and \( y \) axes for reference.
**Answer Format:**
Your Answer: [Answer in two decimal places] [SI units]
Fill in the answer box with your calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9916991e-d642-4c92-a5af-2aa970654239%2F197d8882-d5f9-4aac-a413-bee9914699e9%2Feepekt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 24: Buoyancy and Air Force on a Balloon**
A 580-kg balloon experiences a buoyancy force \( F = 6 \, \text{kN} \). The air force acting on the balloon is defined by the equation:
\[
F_{\text{air}} = \{ C_1 \cdot t \, i - C_2 \cdot \sqrt{t} \, j \} \, \text{N}
\]
where \( t \) is time in seconds, and the constants are \( C_1 = 24 \) and \( C_2 = 240 \).
**Task:** If the balloon starts from rest, determine its speed after 28 seconds. Neglect the size of the balloon but do not neglect its weight. Ensure your answer includes two decimal places and uses proper SI units. Assume \( g = 9.81 \, \text{m/s}^2 \).
**Diagram Explanation:**
- The diagram shows a hot air balloon with upward buoyancy force \( F = 6 \, \text{kN} \).
- Axis system is shown with \( x \) and \( y \) axes for reference.
**Answer Format:**
Your Answer: [Answer in two decimal places] [SI units]
Fill in the answer box with your calculation.
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