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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. Looking for: distance in km, angle in degrees west of nort

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. Looking for: distance in km, angle in degrees west of nort

College Physics
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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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. Looking for: distance in km, angle in degrees west of north. 

### Vector Addition and Direction Illustration The diagram provided illustrates the concept of vector addition and direction in a coordinate system. The vectors are depicted as arrows with specific directions and magnitudes within the Cartesian plane. #### Key Components of the Diagram: 1. **Coordinate System**: - The horizontal axis (x-axis) measures distances in kilometers (km). - The vertical axis (y-axis) also measures distances in kilometers (km). - Points are labeled as O (origin), A, B, and C. 2. **Vectors**: - Four vectors are shown in the figure originating or terminating at different points. - **Vector \(\vec{a}\)** originates from point O (0,0) to point A (150 km, 0 km). It makes an angle of \(30^\circ\) with the positive x-axis. - **Vector \(\vec{b}\)** starts from point A and goes to point B. It is directed 20 degrees north of the y-axis. - **Vector \(\vec{c}\)** continues from point B, pointing straight west to point C. - **Vector \(\vec{R}\)** completes the polygon by returning from point C to the origin O, running 250 km south. 3. **Direction Compass**: - There is a small compass at the upper right corner indicating cardinal directions (North, South, East, and West). 4. **Angles**: - Angle measurements provided give additional context to the vector directions: - \(30^\circ\) between vector \(\vec{a}\) and the x-axis. - \(20^\circ\) between vector \(\vec{b}\) and the negative y-axis. - A supplementary angle of \(110^\circ\) between the horizontal line extending from point A and vector \(\vec{b}\). #### Graphical Explanation: - This graphical representation helps in understanding how vectors are added polygonically by placing them head to tail. - The coordinate grid with labeled distances enables precise determination of vector magnitudes. - The angles provided help in determining the direction of each vector relative to the coordinate axes. Understanding this diagram is crucial in the study of vector operations in physics and engineering, as it visually conveys how vectors summate to resultant vectors through geometric representation.
Transcribed Image Text:### Vector Addition and Direction Illustration The diagram provided illustrates the concept of vector addition and direction in a coordinate system. The vectors are depicted as arrows with specific directions and magnitudes within the Cartesian plane. #### Key Components of the Diagram: 1. **Coordinate System**: - The horizontal axis (x-axis) measures distances in kilometers (km). - The vertical axis (y-axis) also measures distances in kilometers (km). - Points are labeled as O (origin), A, B, and C. 2. **Vectors**: - Four vectors are shown in the figure originating or terminating at different points. - **Vector \(\vec{a}\)** originates from point O (0,0) to point A (150 km, 0 km). It makes an angle of \(30^\circ\) with the positive x-axis. - **Vector \(\vec{b}\)** starts from point A and goes to point B. It is directed 20 degrees north of the y-axis. - **Vector \(\vec{c}\)** continues from point B, pointing straight west to point C. - **Vector \(\vec{R}\)** completes the polygon by returning from point C to the origin O, running 250 km south. 3. **Direction Compass**: - There is a small compass at the upper right corner indicating cardinal directions (North, South, East, and West). 4. **Angles**: - Angle measurements provided give additional context to the vector directions: - \(30^\circ\) between vector \(\vec{a}\) and the x-axis. - \(20^\circ\) between vector \(\vec{b}\) and the negative y-axis. - A supplementary angle of \(110^\circ\) between the horizontal line extending from point A and vector \(\vec{b}\). #### Graphical Explanation: - This graphical representation helps in understanding how vectors are added polygonically by placing them head to tail. - The coordinate grid with labeled distances enables precise determination of vector magnitudes. - The angles provided help in determining the direction of each vector relative to the coordinate axes. Understanding this diagram is crucial in the study of vector operations in physics and engineering, as it visually conveys how vectors summate to resultant vectors through geometric representation.
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