**Problem Description:**A commuter airplane starts from an airport and takes the route shown in the diagram 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 at 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.**Diagram Explanation:**- The diagram includes a coordinate grid with the y-axis representing the north direction and the x-axis representing the east direction.- Starting point \( O \) is at the origin of this grid.- The first leg of the journey, vector \( \vec{A} \), is a line from \( O \) heading 30.0° north of east for a distance of 175 km.- The second leg of the journey, vector \( \vec{B} \), is a line beginning at city \( A \), heading 150 km at 20.0° west of north to city \( B \).- The final leg, vector \( \vec{C} \), is a due west line from city \( B \) to city \( C \) covering 190 km.- The diagram also includes a compass rose indicating cardinal directions (N, E, S, W) and angles corresponding to vector directions.- Vector \( \vec{R} \) is shown as the resultant vector from \( O \) to \( C \).**Inputs:**- Distance: _______ km- Angle: _______° west of northYour goal is to calculate the straight-line distance and angle from the starting point to city \( C \).

Given: a=175 km, θx=30° The free-body diagram of the airplane is

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 R y (km) 950 200 150 00- west of north 0 C b WE 20.0° 110° 7 30.0⁰ 50 100 150 200 x (km)

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 R y (km) 950 200 150 00- west of north 0 C b WE 20.0° 110° 7 30.0⁰ 50 100 150 200 x (km)

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

**Problem Description:**

A commuter airplane starts from an airport and takes the route shown in the diagram 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 at 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.

**Diagram Explanation:**

- The diagram includes a coordinate grid with the y-axis representing the north direction and the x-axis representing the east direction.

- Starting point \( O \) is at the origin of this grid.

- The first leg of the journey, vector \( \vec{A} \), is a line from \( O \) heading 30.0° north of east for a distance of 175 km.

- The second leg of the journey, vector \( \vec{B} \), is a line beginning at city \( A \), heading 150 km at 20.0° west of north to city \( B \).

- The final leg, vector \( \vec{C} \), is a due west line from city \( B \) to city \( C \) covering 190 km.

- The diagram also includes a compass rose indicating cardinal directions (N, E, S, W) and angles corresponding to vector directions.

- Vector \( \vec{R} \) is shown as the resultant vector from \( O \) to \( C \).

**Inputs:**

- Distance: _______ km

- Angle: _______° west of north

Your goal is to calculate the straight-line distance and angle from the starting point to city \( C \).

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