### Airplane Navigation Problem#### Problem Statement:A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.#### Inputs:- Distance covered during each leg of the trip.- Angles indicating the direction of each leg of the trip relative to cardinal directions.#### Inputs to Find:- Distance: ______ km- Angle: ______ ° west of north#### Diagram Explanation:The diagram represents the path taken by the airplane on an xy-coordinate system:1. **Starting Point \( O \):** The initial point of the airplane.2. **Segment \( \vec{a} \):** The airplane travels 175 km from point \( O \) to point \( A \) in a direction of 30.0° north of east. - Vector \( \vec{a} \): - Magnitude: 175 km - Direction: 30.0° north of east3. **Segment \( \vec{b} \):** From point \( A \), the airplane travels 150 km to point \( B \) in a direction of 20.0° west of north. - Vector \( \vec{b} \): - Magnitude: 150 km - Direction: 20.0° west of north4. **Segment \( \vec{c} \):** From point \( B \), the airplane flies 190 km due west to point \( C \). - Vector \( \vec{c} \): - Magnitude: 190 km - Direction: Due west (270° from north)#### Coordinate System:- The x-axis represents the east-west direction (positive x towards east).- The y-axis represents the north-south direction (positive y towards north).- Angles are measured from the north direction (upward y-axis).The coordinate positions to be found are \( x \) and \( y \) coordinates of city C relative to the starting point \( O \).Important notations:- \( \vec{R} \

Given data: Distance = 175 km away Direction =30° north of east second distance =150 km Direction…

A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point. distance km angle ° west of north y (km) 250 - B W E 200 20.0° 150 R 00 110° 30.0° Ix (km) 50 100 150 200

A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point. distance km angle ° west of north y (km) 250 - B W E 200 20.0° 150 R 00 110° 30.0° Ix (km) 50 100 150 200

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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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

### Airplane Navigation Problem

#### Problem Statement:
A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.

#### Inputs:
- Distance covered during each leg of the trip.
- Angles indicating the direction of each leg of the trip relative to cardinal directions.

#### Inputs to Find:
- Distance: ______ km
- Angle: ______ ° west of north

#### Diagram Explanation:
The diagram represents the path taken by the airplane on an xy-coordinate system:

1. **Starting Point \( O \):** The initial point of the airplane.
2. **Segment \( \vec{a} \):** The airplane travels 175 km from point \( O \) to point \( A \) in a direction of 30.0° north of east.
- Vector \( \vec{a} \):
- Magnitude: 175 km
- Direction: 30.0° north of east
3. **Segment \( \vec{b} \):** From point \( A \), the airplane travels 150 km to point \( B \) in a direction of 20.0° west of north.
- Vector \( \vec{b} \):
- Magnitude: 150 km
- Direction: 20.0° west of north
4. **Segment \( \vec{c} \):** From point \( B \), the airplane flies 190 km due west to point \( C \).
- Vector \( \vec{c} \):
- Magnitude: 190 km
- Direction: Due west (270° from north)

#### Coordinate System:
- The x-axis represents the east-west direction (positive x towards east).
- The y-axis represents the north-south direction (positive y towards north).
- Angles are measured from the north direction (upward y-axis).

The coordinate positions to be found are \( x \) and \( y \) coordinates of city C relative to the starting point \( O \).

Important notations:
- \( \vec{R} \

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