39. A 58 kg pole vaulter needs to vault a height of 6.0 m. Assuming that all his kinetic energy can be used for the vault, what is the speed that the vaulter must be traveling in order to clear this height? Ignore the elastic potential of the bent pole. A. 9.8 m/s B. 15 m/s C. 11 m/s D. 36 m/s
39. A 58 kg pole vaulter needs to vault a height of 6.0 m. Assuming that all his kinetic energy can be used for the vault, what is the speed that the vaulter must be traveling in order to clear this height? Ignore the elastic potential of the bent pole. A. 9.8 m/s B. 15 m/s C. 11 m/s D. 36 m/s
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
39. A 58 kg pole vaulter needs to vault a height of 6.0 m. Assuming that all his kinetic energy can be used for the vault, what is the speed that the vaulter must be traveling in order to clear this height? Ignore the elastic potential of the bent pole.
A. 9.8 m/s
B. 15 m/s
C. 11 m/s
D. 36 m/s
Transcribed Image Text:**Question 39:**
A 58 kg pole vaulter needs to vault a height of 6.0 m. Assuming that all his kinetic energy can be used for the vault, what is the speed that the vaulter must be traveling in order to clear this height? Ignore the elastic potential energy of the bent pole.
**Options:**
A. 9.8 m/s
B. 15 m/s
C. 11 m/s
D. 36 m/s
**Unit 5: Energy, Work, and Power**
*Note: The question is presented in a multiple-choice format, exploring concepts related to kinetic and potential energy. It challenges students to apply energy conservation principles to determine the necessary speed for achieving a specified vault height.*
![### Problem 39:
A 58 kg pole vaulter needs to vault a height of 6.0 m. Assuming that all his kinetic energy can be used for the vault, what is the speed that the vaulter must be traveling in order to clear this height? Ignore the elastic potential energy of the bent pole.
#### Options:
- **A.** 9.8 m/s
- **B.** 15 m/s
- **C.** 11 m/s
- **D.** 36 m/s
---
### Explanation:
In this problem, we are asked to determine the speed a pole vaulter needs to achieve to clear a height of 6.0 meters, given his mass is 58 kg. We can solve this by equating the kinetic energy required to the potential energy at the peak of the vault.
The key principle here is the conservation of energy:
- **Kinetic Energy (KE):**
\[
KE = \frac{1}{2}mv^2
\]
- **Potential Energy (PE):**
\[
PE = mgh
\]
Where:
- \( m = 58 \, \text{kg} \) (mass of the vaulter)
- \( v \) = speed needed (unknown)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 6.0 \, \text{m} \) (height to be vaulted)
By equating kinetic and potential energy (\( KE = PE \)), we find:
\[
\frac{1}{2}mv^2 = mgh
\]
Solving for \( v \):
\[
v = \sqrt{2gh}
\]
Plugging in the values:
\[
v = \sqrt{2 \times 9.8 \, \text{m/s}^2 \times 6.0 \, \text{m}} \approx 10.84 \, \text{m/s}
\]
Thus, the closest answer is **C. 11 m/s**.
### Unit Reference:
This problem relates to Unit 5: Energy, Work, and Power, focusing on the principles of conservation of energy in physical systems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f0a8c67-ba07-4933-95fd-7d397a6626d9%2F7522953b-d1cd-4a39-ba31-6dc84224a954%2Febde8l4_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 39:
A 58 kg pole vaulter needs to vault a height of 6.0 m. Assuming that all his kinetic energy can be used for the vault, what is the speed that the vaulter must be traveling in order to clear this height? Ignore the elastic potential energy of the bent pole.
#### Options:
- **A.** 9.8 m/s
- **B.** 15 m/s
- **C.** 11 m/s
- **D.** 36 m/s
---
### Explanation:
In this problem, we are asked to determine the speed a pole vaulter needs to achieve to clear a height of 6.0 meters, given his mass is 58 kg. We can solve this by equating the kinetic energy required to the potential energy at the peak of the vault.
The key principle here is the conservation of energy:
- **Kinetic Energy (KE):**
\[
KE = \frac{1}{2}mv^2
\]
- **Potential Energy (PE):**
\[
PE = mgh
\]
Where:
- \( m = 58 \, \text{kg} \) (mass of the vaulter)
- \( v \) = speed needed (unknown)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 6.0 \, \text{m} \) (height to be vaulted)
By equating kinetic and potential energy (\( KE = PE \)), we find:
\[
\frac{1}{2}mv^2 = mgh
\]
Solving for \( v \):
\[
v = \sqrt{2gh}
\]
Plugging in the values:
\[
v = \sqrt{2 \times 9.8 \, \text{m/s}^2 \times 6.0 \, \text{m}} \approx 10.84 \, \text{m/s}
\]
Thus, the closest answer is **C. 11 m/s**.
### Unit Reference:
This problem relates to Unit 5: Energy, Work, and Power, focusing on the principles of conservation of energy in physical systems.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON