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If you double the kinetic energy of an arrow, by what factor does its speed increase?
- a)2
- b)4
- c)√2
- d)None
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If you double the kinetic energy of an arrow, by what factor does its ...
Understanding Kinetic Energy
Kinetic energy (KE) is the energy that an object possesses due to its motion. The formula for kinetic energy is:
- KE = (1/2) m v²
Where:
- m = mass of the object
- v = velocity (speed) of the object
Doubling the Kinetic Energy
When we say that the kinetic energy of the arrow is doubled, we can express this mathematically:
- 2 * KE = 2 * (1/2) m v²
- This simplifies to: KE' = m v'²
Where KE' is the new kinetic energy and v' is the new speed.
Setting Up the Equation
From the original equation:
- m v'² = 2 * (1/2) m v²
We can simplify this by canceling out the mass (m) from both sides, as long as it is not zero:
- v'² = 2 v²
Finding the New Speed
To find the new speed (v'), we take the square root of both sides:
- v' = √(2) * v
This indicates that when the kinetic energy is doubled, the new speed (v') is √2 times the original speed (v).
Conclusion
Thus, the factor by which the speed increases when the kinetic energy of the arrow is doubled is:
- √2 (option C)
This means the speed increases by a factor of approximately 1.414, which is the square root of 2.
Kinetic energy (KE) is the energy that an object possesses due to its motion. The formula for kinetic energy is:
- KE = (1/2) m v²
Where:
- m = mass of the object
- v = velocity (speed) of the object
Doubling the Kinetic Energy
When we say that the kinetic energy of the arrow is doubled, we can express this mathematically:
- 2 * KE = 2 * (1/2) m v²
- This simplifies to: KE' = m v'²
Where KE' is the new kinetic energy and v' is the new speed.
Setting Up the Equation
From the original equation:
- m v'² = 2 * (1/2) m v²
We can simplify this by canceling out the mass (m) from both sides, as long as it is not zero:
- v'² = 2 v²
Finding the New Speed
To find the new speed (v'), we take the square root of both sides:
- v' = √(2) * v
This indicates that when the kinetic energy is doubled, the new speed (v') is √2 times the original speed (v).
Conclusion
Thus, the factor by which the speed increases when the kinetic energy of the arrow is doubled is:
- √2 (option C)
This means the speed increases by a factor of approximately 1.414, which is the square root of 2.
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Community Answer
If you double the kinetic energy of an arrow, by what factor does its ...
Kinetic energy depends upon velocity and mass. The relation between K.E with mass and velocity is K.E = 0.5mv2. If we double the kinetic energy, the velocity has to be increased by a factor equal to the square root of two.
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If you double the kinetic energy of an arrow, by what factor does its speed increase?a)2b)4c)√2d)NoneCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If you double the kinetic energy of an arrow, by what factor does its speed increase?a)2b)4c)√2d)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If you double the kinetic energy of an arrow, by what factor does its speed increase?a)2b)4c)√2d)NoneCorrect answer is option 'C'. Can you explain this answer?.
If you double the kinetic energy of an arrow, by what factor does its speed increase?a)2b)4c)√2d)NoneCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If you double the kinetic energy of an arrow, by what factor does its speed increase?a)2b)4c)√2d)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If you double the kinetic energy of an arrow, by what factor does its speed increase?a)2b)4c)√2d)NoneCorrect answer is option 'C'. Can you explain this answer?.
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