At the instant shown, cars A and Bare traveling at speeds of 55 mi / hand 40 mi / h. respectively. Bis increasing its speed by 1200 mi/h, while A maintains a constant speed. Car B moves along a curve having a radius of curvature of 0.5 mi. Vg = 40 mi/h vA = 55 mi/h Part A Determine the magnitude of the velocity of B with respect to A. Express your answer to three significant figures and include the appropriate units. Part B Determine the angle 0, of vRIA (counterclockwise from the positive z axcis). Express your answer to three significant figures and include the appropriate units. Part C Determine the magnitude of the acceleration of Bwith respect to A. Express your answer to three significant figures and include the appropriate units. Part D Determine the angle 0, of apa (counterclockwise from the positive z axis). Express your answer to three significant figures and include the appropriate units.
At the instant shown, cars A and Bare traveling at speeds of 55 mi / hand 40 mi / h. respectively. Bis increasing its speed by 1200 mi/h, while A maintains a constant speed. Car B moves along a curve having a radius of curvature of 0.5 mi. Vg = 40 mi/h vA = 55 mi/h Part A Determine the magnitude of the velocity of B with respect to A. Express your answer to three significant figures and include the appropriate units. Part B Determine the angle 0, of vRIA (counterclockwise from the positive z axcis). Express your answer to three significant figures and include the appropriate units. Part C Determine the magnitude of the acceleration of Bwith respect to A. Express your answer to three significant figures and include the appropriate units. Part D Determine the angle 0, of apa (counterclockwise from the positive z axis). Express your answer to three significant figures and include the appropriate units.
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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![### Relative Motion Analysis (Cars)
#### Problem Statement:
At the instant shown, cars A and B are traveling at speeds of 55 mi/h and 40 mi/h, respectively. Car B is increasing its speed by 1200 mi/h², while car A maintains a constant speed. Car B moves along a curve having a radius of curvature of 0.5 mi.
#### Diagram:
The given diagram shows two cars, A and B. Car A is traveling at 55 mi/h along a straight path, while car B is traveling at 40 mi/h along a curved path with a radius of curvature of 0.5 mi. The angle between the direction of car B's motion and the x-axis is 30°.
### Part A:
Determine the magnitude of the velocity of \( B \) with respect to \( A \).
- Express your answer to three significant figures and include the appropriate units.
\[ v_{B/A} = \boxed{ \hspace{4cm} } \, \text{mi/h} \]
### Part B:
Determine the angle \( \theta_{B/A} \) of \( \mathbf{v}_{B/A} \) (counterclockwise from the positive x-axis).
- Express your answer to three significant figures and include the appropriate units.
\[ \theta_{B/A} = \boxed{ \hspace{4cm} } \, ^\circ \]
### Part C:
Determine the magnitude of the acceleration of \( B \) with respect to \( A \).
- Express your answer to three significant figures and include the appropriate units.
\[ a_{B/A} = \boxed{ \hspace{4cm} } \, \text{mi/h}^2 \]
### Part D:
Determine the angle \( \phi_{B/A} \) of \( \mathbf{a}_{B/A} \) (counterclockwise from the positive x-axis).
- Express your answer to three significant figures and include the appropriate units.
\[ \phi_{B/A} = \boxed{ \hspace{4cm} } \, ^\circ \]
### Explanation of the Diagram:
- Car A is shown traveling on a linear path at 55 mi/h.
- Car B is traveling on a curved path at 40 mi/h, with an increase in speed of 1200 mi/h².
- The curve along which car B is traveling has a radius of curvature](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f88d8b4-ac68-457e-9d02-d311a9616c7b%2F14d5c70d-2acb-4d17-8aca-b2675892cf1b%2Fosxzqh4_processed.png&w=3840&q=75)
Transcribed Image Text:### Relative Motion Analysis (Cars)
#### Problem Statement:
At the instant shown, cars A and B are traveling at speeds of 55 mi/h and 40 mi/h, respectively. Car B is increasing its speed by 1200 mi/h², while car A maintains a constant speed. Car B moves along a curve having a radius of curvature of 0.5 mi.
#### Diagram:
The given diagram shows two cars, A and B. Car A is traveling at 55 mi/h along a straight path, while car B is traveling at 40 mi/h along a curved path with a radius of curvature of 0.5 mi. The angle between the direction of car B's motion and the x-axis is 30°.
### Part A:
Determine the magnitude of the velocity of \( B \) with respect to \( A \).
- Express your answer to three significant figures and include the appropriate units.
\[ v_{B/A} = \boxed{ \hspace{4cm} } \, \text{mi/h} \]
### Part B:
Determine the angle \( \theta_{B/A} \) of \( \mathbf{v}_{B/A} \) (counterclockwise from the positive x-axis).
- Express your answer to three significant figures and include the appropriate units.
\[ \theta_{B/A} = \boxed{ \hspace{4cm} } \, ^\circ \]
### Part C:
Determine the magnitude of the acceleration of \( B \) with respect to \( A \).
- Express your answer to three significant figures and include the appropriate units.
\[ a_{B/A} = \boxed{ \hspace{4cm} } \, \text{mi/h}^2 \]
### Part D:
Determine the angle \( \phi_{B/A} \) of \( \mathbf{a}_{B/A} \) (counterclockwise from the positive x-axis).
- Express your answer to three significant figures and include the appropriate units.
\[ \phi_{B/A} = \boxed{ \hspace{4cm} } \, ^\circ \]
### Explanation of the Diagram:
- Car A is shown traveling on a linear path at 55 mi/h.
- Car B is traveling on a curved path at 40 mi/h, with an increase in speed of 1200 mi/h².
- The curve along which car B is traveling has a radius of curvature
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