### 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)...

See similar textbooks

Similar questions

A ferry transports tourists among three islands. It sails from the first island to the second island, 5.89 km away, in a direction 37.0 north of east. It then sails from the second island to the third island in a direction 74.5° west of north. Finally, it returns to the first island, sailing in a direction 28.0" east of south (a) Calculate the distance between the second and third islands. km (b) Calculate the distance between the first and third islands. km
A plane takes off from an airport and flies to town A, located d₁ = 340 km from the airport in the direction 20.0° north of east. The plane then flies to town B, located d₂ 210 km at 30.0° west of north from town A. Use graphical methods to determine the distance and direction from town B to the airport. (Enter the distance in km and the direction in degrees south of west.) km o south of west - distance direction
Suppose you walk 14.5 m in a direction exactly 19° south of west then you walk 22 m in a direction exactly 39° west of north. How far are you from your starting point in m? Please explain how you got your answer in detail.
An airplane flies 200 km due west from city A to city B and then 285 km in the direction of 33.0° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? km(b) Relative to city A, in what direction is city C? ° north of west
Vector A: Magnitude: .6769 N, angle: 0 degrees Vector B: Magnitude: 1.265 N, angle: 140 degrees Vector C: Magnitude: .7358 N, angle: 235 degrees Vector D: Magnitude: .7063, angle: 340 degrees Create a diagram and use vector polygon to find the resultant vector.
What is the displacement and direction of the resultant vector if a soccer player runs 55.0m at an angle of N27 degrees West, and then runs 23.0m at an angle of S5 degrees West from her new location? Draw a diagram, please!
You drive 5.50 km in a straight line in a direction 30.5° east of north. Find the distances you would have to drive straight east and then straight north to arrive at the same point. What distance should you drive straight east? What distance should you drive straight north?
A person leaves home and walks 6 miles west, then 5 miles southwest. How far from home is she? Round to at least one decimal place. miles In what direction must she walk to head directly home? Round to at least one decimal place. degrees North of East
bn nas set his GPS to track his route. At the end of his hike, his GPS indicates that he walked 3.50 miles north, 1.00 miles at 45 degrees north of east, and 1.50 miles south. How far away is Bill from his starting position? And in what direction is he? Provide the direction in number of degrees in reference to the cardinal directions (North of East, South of West, etc.).
A person walks 26.0° north of east for 3.70 km. How far due north and how far due east would she have to walk to arrive at the same location? north km east km
On his trip from home to school, Noah Omwerk drives along three streets after exiting the driveway. He drives 1.85 miles south, 2.43 miles east and 0.35 miles north. Determine the magnitude of Noah's resultant displacement. And the angle from East to South.