I don't understand how you're getting the Ax

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)...
icon
Related questions
Question

I don't understand how you're getting the Ax 

## Diagram Explanation and Calculation

### Diagram Description
The provided diagram depicts a right-angled triangle where the following components are identified:

- The hypotenuse (A) measures 1.5 km.
- The opposite side (A_y) and the adjacent side (A_x) are the sides of the triangle with respect to the 45° angle. 
- The adjacent side (A_x) is given as -√2 km (approximately -20 km).
- The opposite side (A_y) is to be determined.
  
### Point Coordinates
The coordinates of the point are (x=0 km, y=1.06 km).

### Given
\[ A = 1.5 \, \text{km} \]
\[ A_x = -20 \, \text{km} \]
\[ \theta = 45^\circ \]

### Problem
1. To find the component \( A_y \).

### Calculation

To determine \( A_y \):

Using the sine function,
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
\[ \sin(45^\circ) = \frac{A_y}{1.5 \, \text{km}} \]
\[ \frac{\sqrt{2}}{2} = \frac{A_y}{1.5 \, \text{km}} \]

Solving for \( A_y \):
\[ A_y = \left( \frac{\sqrt{2}}{2} \right) \times 1.5\, \text{km} \]
\[ A_y = \frac{1.5 \sqrt{2}}{2} \]
\[ A_y \approx 1.06 \, \text{km} \]

Thus,
\[ A_y = 1.06 \, \text{km} \]

This calculation shows that the vertical component \( A_y \) of the vector is approximately 1.06 km.

### Summary
The length of \( A_y \) obtained from the given diagram and calculations is:
\[ \boxed{A_y = 1.06 \, \text{km}} \]
Transcribed Image Text:## Diagram Explanation and Calculation ### Diagram Description The provided diagram depicts a right-angled triangle where the following components are identified: - The hypotenuse (A) measures 1.5 km. - The opposite side (A_y) and the adjacent side (A_x) are the sides of the triangle with respect to the 45° angle. - The adjacent side (A_x) is given as -√2 km (approximately -20 km). - The opposite side (A_y) is to be determined. ### Point Coordinates The coordinates of the point are (x=0 km, y=1.06 km). ### Given \[ A = 1.5 \, \text{km} \] \[ A_x = -20 \, \text{km} \] \[ \theta = 45^\circ \] ### Problem 1. To find the component \( A_y \). ### Calculation To determine \( A_y \): Using the sine function, \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] \[ \sin(45^\circ) = \frac{A_y}{1.5 \, \text{km}} \] \[ \frac{\sqrt{2}}{2} = \frac{A_y}{1.5 \, \text{km}} \] Solving for \( A_y \): \[ A_y = \left( \frac{\sqrt{2}}{2} \right) \times 1.5\, \text{km} \] \[ A_y = \frac{1.5 \sqrt{2}}{2} \] \[ A_y \approx 1.06 \, \text{km} \] Thus, \[ A_y = 1.06 \, \text{km} \] This calculation shows that the vertical component \( A_y \) of the vector is approximately 1.06 km. ### Summary The length of \( A_y \) obtained from the given diagram and calculations is: \[ \boxed{A_y = 1.06 \, \text{km}} \]
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Relativistic speed and time
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.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
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…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON