14. A constant force of 10 newtons is being applied at a constant angle of 45° on an object at the same time that a constant force of 20 newtons at a constant angle of 65° is acting on the object. What is the magnitude and direction of the resultant force? 14.
14. A constant force of 10 newtons is being applied at a constant angle of 45° on an object at the same time that a constant force of 20 newtons at a constant angle of 65° is acting on the object. What is the magnitude and direction of the resultant force? 14.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Vector and Force Problems
#### Problem 14:
A constant force of 10 newtons is being applied at a constant angle of 45° on an object at the same time that a constant force of 20 newtons at a constant angle of 65° is acting on the object. What is the magnitude and direction of the resultant force?
\[14. \quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]
#### Problem 15:
An airplane is traveling due east with a velocity of 580 miles per hour. The wind blows at 50 miles per hour at an angle of 45° to the horizontal. Determine the velocity of the airplane's flight.
\[15. \quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]
#### Problem 16:
A cruise ship's path travels for 16.1 miles at an angle of 60.3°. It then follows a path that can be represented by the vector \(\langle 22, 7 \rangle\). What is the resultant path?
\[16. \quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]
#### Problem 17:
Find the projection of \(\mathbf{u} = \langle 9, -5 \rangle\) onto \(\mathbf{v} = \langle 3, -2 \rangle\).
\[17. \quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]
### Explanation of Diagrams or Graphs (if applicable):
There are no diagrams or graphs provided in this section. The problems are purely text-based and focus on vector mathematics and force calculations. Students are expected to use their understanding of vectors, trigonometry, and physics principles to solve these problems. The use of diagrams or sketches to visualize the vectors and forces may aid in better comprehension and problem-solving strategy.
### Additional Notes:
1. **For Problem 14**: Decompose each force into its horizontal and vertical components using trigonometric functions. Then, sum the respective components to find the resultant vector.
2. **For Problem 15**: Decompose the velocity of the wind into its eastward and northward components. Combine these components with the airplane's initial eastward velocity to find the resultant velocity vector.
3. **For Problem 16**: Convert the cruise ship's initial path into a vector form and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b3799ad-3ea5-4cad-a42a-63419fcded6b%2F7e5167b8-844e-437b-a9b0-9d69f0531969%2Fm20t30f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector and Force Problems
#### Problem 14:
A constant force of 10 newtons is being applied at a constant angle of 45° on an object at the same time that a constant force of 20 newtons at a constant angle of 65° is acting on the object. What is the magnitude and direction of the resultant force?
\[14. \quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]
#### Problem 15:
An airplane is traveling due east with a velocity of 580 miles per hour. The wind blows at 50 miles per hour at an angle of 45° to the horizontal. Determine the velocity of the airplane's flight.
\[15. \quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]
#### Problem 16:
A cruise ship's path travels for 16.1 miles at an angle of 60.3°. It then follows a path that can be represented by the vector \(\langle 22, 7 \rangle\). What is the resultant path?
\[16. \quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]
#### Problem 17:
Find the projection of \(\mathbf{u} = \langle 9, -5 \rangle\) onto \(\mathbf{v} = \langle 3, -2 \rangle\).
\[17. \quad\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]
### Explanation of Diagrams or Graphs (if applicable):
There are no diagrams or graphs provided in this section. The problems are purely text-based and focus on vector mathematics and force calculations. Students are expected to use their understanding of vectors, trigonometry, and physics principles to solve these problems. The use of diagrams or sketches to visualize the vectors and forces may aid in better comprehension and problem-solving strategy.
### Additional Notes:
1. **For Problem 14**: Decompose each force into its horizontal and vertical components using trigonometric functions. Then, sum the respective components to find the resultant vector.
2. **For Problem 15**: Decompose the velocity of the wind into its eastward and northward components. Combine these components with the airplane's initial eastward velocity to find the resultant velocity vector.
3. **For Problem 16**: Convert the cruise ship's initial path into a vector form and
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