College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![### Vector Projections and Magnitude Calculation
#### (b) Calculate the Projections of \(\overrightarrow{OP}\)
To project the vector \(\overrightarrow{OP}\) along the \(x'\) and \(y'\) directions:
- Enter the projection on the \(x'\) axis: \((\overrightarrow{OP})_{x'} =\) [Input Box] cm
- Enter the projection on the \(y'\) axis: \((\overrightarrow{OP})_{y'} =\) [Input Box] cm
Ensure values are entered to 2 significant figures.
---
#### (c) Use the Projections to Calculate Magnitude along \(x\) and \(y\) Directions
To find the magnitude of \(\overrightarrow{OP}\):
\[ \overrightarrow{OP} = \sqrt{((OP)_x)^2 + ((OP)_y)^2} \]
- Enter the magnitude: \(OP =\) [Input Box] cm
Values should be entered to 2 significant figures.
---
#### (d) Use the Projections to Calculate Magnitude along \(x'\) and \(y'\) Directions
Similarly, to calculate the magnitude of \(\overrightarrow{OP}\) along the \(x'\) and \(y'\) directions:
\[ \overrightarrow{OP} = \sqrt{((OP)_{x'})^2 + ((OP)_{y'})^2} \]
- Enter the magnitude: \(OP =\) [Input Box] cm
Values should be entered to 2 significant figures.](https://content.bartleby.com/qna-images/question/8512e4d2-f559-44cb-9fee-36fee0c29e9a/a7e3f537-6a67-44e5-87f2-1beec167e712/z2jwqah_processed.png)
Transcribed Image Text:### Vector Projections and Magnitude Calculation
#### (b) Calculate the Projections of \(\overrightarrow{OP}\)
To project the vector \(\overrightarrow{OP}\) along the \(x'\) and \(y'\) directions:
- Enter the projection on the \(x'\) axis: \((\overrightarrow{OP})_{x'} =\) [Input Box] cm
- Enter the projection on the \(y'\) axis: \((\overrightarrow{OP})_{y'} =\) [Input Box] cm
Ensure values are entered to 2 significant figures.
---
#### (c) Use the Projections to Calculate Magnitude along \(x\) and \(y\) Directions
To find the magnitude of \(\overrightarrow{OP}\):
\[ \overrightarrow{OP} = \sqrt{((OP)_x)^2 + ((OP)_y)^2} \]
- Enter the magnitude: \(OP =\) [Input Box] cm
Values should be entered to 2 significant figures.
---
#### (d) Use the Projections to Calculate Magnitude along \(x'\) and \(y'\) Directions
Similarly, to calculate the magnitude of \(\overrightarrow{OP}\) along the \(x'\) and \(y'\) directions:
\[ \overrightarrow{OP} = \sqrt{((OP)_{x'})^2 + ((OP)_{y'})^2} \]
- Enter the magnitude: \(OP =\) [Input Box] cm
Values should be entered to 2 significant figures.
![### Problem Statement:
Please answer the following question(s):
1.
The vector \(\overrightarrow{OP}\) shown in the figure has a length of 4.0 cm. Two sets of perpendicular axes, \(x-y\) and \(x'-y'\), are shown. Express \(\overrightarrow{OP}\) in terms of its \(x\) and \(y\) components in each set of axes.
#### (a) Calculate the projections of \(\overrightarrow{OP}\) along the \(x\) and \(y\) directions.
Enter to 2 significant figures:
\[
(\overrightarrow{OP})_x = \_\_\_\, \text{cm}
\]
\[
(\overrightarrow{OP})_y = \_\_\_\, \text{cm}
\]
---
### Graph Explanation:
The provided diagram shows two sets of axes: \(x-y\) and \(x'-y'\). Both sets are perpendicular to each other. The vector \(\overrightarrow{OP}\) originates at point \(O\) and terminates at point \(P\). The diagram indicates that the vector makes an angle of 30 degrees with both the \(x\) and \(x'\) axes.
In detail:
- The \(x\) and \(x'\) axes are horizontal.
- The \(y\) and \(y'\) axes are vertical.
- \(\overrightarrow{OP}\) is directed at an angle of 30 degrees upwards from the \(x\) axis.
- An identical angle of 30 degrees is shown from the \(x'\) axis in the rotated coordinate system.](https://content.bartleby.com/qna-images/question/8512e4d2-f559-44cb-9fee-36fee0c29e9a/a7e3f537-6a67-44e5-87f2-1beec167e712/8g6v62_processed.png)
Transcribed Image Text:### Problem Statement:
Please answer the following question(s):
1.
The vector \(\overrightarrow{OP}\) shown in the figure has a length of 4.0 cm. Two sets of perpendicular axes, \(x-y\) and \(x'-y'\), are shown. Express \(\overrightarrow{OP}\) in terms of its \(x\) and \(y\) components in each set of axes.
#### (a) Calculate the projections of \(\overrightarrow{OP}\) along the \(x\) and \(y\) directions.
Enter to 2 significant figures:
\[
(\overrightarrow{OP})_x = \_\_\_\, \text{cm}
\]
\[
(\overrightarrow{OP})_y = \_\_\_\, \text{cm}
\]
---
### Graph Explanation:
The provided diagram shows two sets of axes: \(x-y\) and \(x'-y'\). Both sets are perpendicular to each other. The vector \(\overrightarrow{OP}\) originates at point \(O\) and terminates at point \(P\). The diagram indicates that the vector makes an angle of 30 degrees with both the \(x\) and \(x'\) axes.
In detail:
- The \(x\) and \(x'\) axes are horizontal.
- The \(y\) and \(y'\) axes are vertical.
- \(\overrightarrow{OP}\) is directed at an angle of 30 degrees upwards from the \(x\) axis.
- An identical angle of 30 degrees is shown from the \(x'\) axis in the rotated coordinate system.
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