Type The Correct Answer In The Box.What's The Velocity Of The Balloon? Use $V=\sqrt{\frac{2 K R}{\text{nt}}}$.A Hot-air Balloon With A Mass Of 400 Kilograms Moves Across The Sky With 3,200 Joules Of Kinetic Energy. The Velocity Of The
Understanding the Problem
In this problem, we are given a hot-air balloon with a mass of 400 kilograms and 3,200 joules of kinetic energy. We need to calculate the velocity of the balloon using the formula $V=\sqrt{\frac{2 K R}{\text{nt}}}$.
Given Information
- Mass of the balloon (m) = 400 kilograms
- Kinetic energy (K) = 3,200 joules
- We need to find the velocity (V) of the balloon.
The Formula
The formula to calculate the velocity of the balloon is given by $V=\sqrt{\frac{2 K R}{\text{nt}}}$.
Breaking Down the Formula
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V$ is the velocity of the balloon
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K$ is the kinetic energy of the balloon
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R$ is the radius of the balloon (we don't have this information, so we will assume it is not necessary for this problem)
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n$ is a constant (we don't have this information, so we will assume it is not necessary for this problem)
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t$ is the time (we don't have this information, so we will assume it is not necessary for this problem)
Simplifying the Formula
Since we don't have the values of $R$, $n$, and $t$, we can simplify the formula by assuming that they are not necessary for this problem. Therefore, the formula becomes $V=\sqrt{\frac{2 K}{\text{m}}}$.
Plugging in the Values
Now, we can plug in the values of $K$ and $m$ into the simplified formula.
Solving for V
Conclusion
Therefore, the velocity of the hot-air balloon is 4 meters per second.
Discussion
This problem is a classic example of how to calculate the velocity of an object using the formula $V=\sqrt{\frac{2 K}{\text{m}}}$.
- What is the significance of the formula? The formula is used to calculate the velocity of an object when its kinetic energy and mass are known.
- What are the limitations of the formula? The formula assumes that the object is moving in a straight line and that there are no external forces acting on it.
- How can the formula be applied in real-life situations? The formula can be applied in real-life situations such as calculating the velocity of a car or a plane.
References
- Physics for Scientists and Engineers by Paul A. Tipler and Gene Mosca
- University Physics by Hugh D. Young and Roger A. Freedman
Additional Resources
- Khan Academy: Kinetic Energy
- Physics Classroom: Kinetic Energy
- Wikipedia: Kinetic Energy
Q&A: Calculating the Velocity of a Hot-Air Balloon =====================================================
Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions related to calculating the velocity of a hot-air balloon.
Q: What is the significance of the formula V = √(2K/m)?
A: The formula V = √(2K/m) is used to calculate the velocity of an object when its kinetic energy (K) and mass (m) are known. This formula is a fundamental concept in physics and is widely used in various fields such as engineering, mechanics, and astronomy.
Q: What are the limitations of the formula V = √(2K/m)?
A: The formula V = √(2K/m) assumes that the object is moving in a straight line and that there are no external forces acting on it. This means that the formula is not applicable in situations where the object is accelerating or decelerating, or where there are external forces such as friction or air resistance.
Q: How can the formula V = √(2K/m) be applied in real-life situations?
A: The formula V = √(2K/m) can be applied in real-life situations such as calculating the velocity of a car or a plane. For example, if you know the kinetic energy of a car and its mass, you can use the formula to calculate its velocity.
Q: What is the difference between kinetic energy and potential energy?
A: Kinetic energy is the energy of motion, while potential energy is the energy of position. In other words, kinetic energy is the energy an object has when it is moving, while potential energy is the energy an object has when it is at rest.
Q: How can I calculate the kinetic energy of an object?
A: The kinetic energy of an object can be calculated using the formula K = (1/2)mv^2, where m is the mass of the object and v is its velocity.
Q: What is the relationship between velocity and kinetic energy?
A: The velocity of an object is directly proportional to the square root of its kinetic energy. This means that as the kinetic energy of an object increases, its velocity also increases.
Q: Can the formula V = √(2K/m) be used to calculate the velocity of an object in a rotating or oscillating motion?
A: No, the formula V = √(2K/m) is only applicable to objects moving in a straight line. If an object is rotating or oscillating, you will need to use a different formula to calculate its velocity.
Q: What are some common applications of the formula V = √(2K/m)?
A: The formula V = √(2K/m) has many common applications in fields such as engineering, mechanics, and astronomy. Some examples include:
- Calculating the velocity of a car or a plane
- Determining the speed of a projectile
- Calculating the velocity of a rotating or oscillating object
- Determining the speed of a satellite or a spacecraft
Conclusion
In this article, we have answered some of the most frequently asked questions related to calculating the velocity of a hot-air balloon. We hope that this article has provided you with a better understanding of the formula V = √(2K/m) and its applications.
References
- Physics for Scientists and Engineers by Paul A. Tipler and Gene Mosca
- University Physics by Hugh D. Young and Roger A. Freedman
- Khan Academy: Kinetic Energy
- Physics Classroom: Kinetic Energy
- Wikipedia: Kinetic Energy
Additional Resources
- Online Physics Tutorials
- Physics Problems and Solutions
- Physics Formulas and Equations