Please answer the following question(s): 1. The vector OP shown in the figure has a length of 9.0 cm. Two sets of perpendicular axes, x- and x' - y', are shown. Express OP in terms of its x and y components in each set of axes. cm (OP)x= (OP) y= (a) Calculate the projections of OP along the x and y directions. Enter to 2 significant figures (OP)x= (OP)y= cm P 30° 30° cm X (b) Calculate the projections of OP along the x' and y' directions. Enter to 2 significant figures cm (C) Use the projections of O along the vand directions to calculate the magnitude of OP
Please answer the following question(s): 1. The vector OP shown in the figure has a length of 9.0 cm. Two sets of perpendicular axes, x- and x' - y', are shown. Express OP in terms of its x and y components in each set of axes. cm (OP)x= (OP) y= (a) Calculate the projections of OP along the x and y directions. Enter to 2 significant figures (OP)x= (OP)y= cm P 30° 30° cm X (b) Calculate the projections of OP along the x' and y' directions. Enter to 2 significant figures cm (C) Use the projections of O along the vand directions to calculate the magnitude of OP
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)...
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![# Vector Projections and Components
**Figure Explanation:**
The figure illustrates vector \(\overrightarrow{OP}\) with a length of 9.0 cm. Two sets of perpendicular axes are depicted: the primary axes \(x-y\) and the rotated axes \(x'-y'\). Vector \(\overrightarrow{OP}\) is at a 30° angle to both the \(x\) and \(x'\) axes.
---
**Problem:**
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:**
\[
(\overrightarrow{OP})_x = \_\_\_\_\_\_ \, \text{cm}
\]
\[
(\overrightarrow{OP})_y = \_\_\_\_\_\_ \, \text{cm}
\]
### (b) Calculate the projections of \(\overrightarrow{OP}\) along the \(x'\) and \(y'\) directions.
- **Enter to 2 significant figures:**
\[
(\overrightarrow{OP})_{x'} = \_\_\_\_\_\_ \, \text{cm}
\]
\[
(\overrightarrow{OP})_{y'} = \_\_\_\_\_\_ \, \text{cm}
\]
---
**Note:**
For both sets of calculations, break down vector \(\overrightarrow{OP}\) using trigonometric functions based on the given angle (30°) and the length of the vector.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bc89b86-0319-465b-96a1-f0c9ce452bb7%2F2b582d31-2988-432e-9120-06d36d956b89%2Fvjmxix_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Vector Projections and Components
**Figure Explanation:**
The figure illustrates vector \(\overrightarrow{OP}\) with a length of 9.0 cm. Two sets of perpendicular axes are depicted: the primary axes \(x-y\) and the rotated axes \(x'-y'\). Vector \(\overrightarrow{OP}\) is at a 30° angle to both the \(x\) and \(x'\) axes.
---
**Problem:**
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:**
\[
(\overrightarrow{OP})_x = \_\_\_\_\_\_ \, \text{cm}
\]
\[
(\overrightarrow{OP})_y = \_\_\_\_\_\_ \, \text{cm}
\]
### (b) Calculate the projections of \(\overrightarrow{OP}\) along the \(x'\) and \(y'\) directions.
- **Enter to 2 significant figures:**
\[
(\overrightarrow{OP})_{x'} = \_\_\_\_\_\_ \, \text{cm}
\]
\[
(\overrightarrow{OP})_{y'} = \_\_\_\_\_\_ \, \text{cm}
\]
---
**Note:**
For both sets of calculations, break down vector \(\overrightarrow{OP}\) using trigonometric functions based on the given angle (30°) and the length of the vector.
![(c) Use the projections of \(\vec{OP}\) along the \(x\) and \(y\) directions to calculate the magnitude of \(\vec{OP}\) using \(\vec{OP} = \sqrt{(OP_x)^2 + (OP_y)^2}\).
Enter to 2 significant figures
\(OP =\) [Text Box] \(\sqrt{}\) cm
(d) Use the projections of \(\vec{OP}\) along the \(x'\) and \(y'\) directions to calculate the magnitude of \(\vec{OP}\) using \(\vec{OP} = \sqrt{(OP_{x'})^2 + (OP_{y'})^2}\).
Enter to 2 significant figures
\(OP =\) [Text Box] \(\sqrt{}\) cm
(e) What can you conclude about the magnitude of a vector with respect to rotated coordinate axes?
The magnitude of the vectors using components in different coordinate axes that are rotated with respect to each other [Drop-down Arrow] change.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bc89b86-0319-465b-96a1-f0c9ce452bb7%2F2b582d31-2988-432e-9120-06d36d956b89%2Fl8p415o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) Use the projections of \(\vec{OP}\) along the \(x\) and \(y\) directions to calculate the magnitude of \(\vec{OP}\) using \(\vec{OP} = \sqrt{(OP_x)^2 + (OP_y)^2}\).
Enter to 2 significant figures
\(OP =\) [Text Box] \(\sqrt{}\) cm
(d) Use the projections of \(\vec{OP}\) along the \(x'\) and \(y'\) directions to calculate the magnitude of \(\vec{OP}\) using \(\vec{OP} = \sqrt{(OP_{x'})^2 + (OP_{y'})^2}\).
Enter to 2 significant figures
\(OP =\) [Text Box] \(\sqrt{}\) cm
(e) What can you conclude about the magnitude of a vector with respect to rotated coordinate axes?
The magnitude of the vectors using components in different coordinate axes that are rotated with respect to each other [Drop-down Arrow] change.
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