College Physics
College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 3, Problem 19P

A commuter airplane starts from ar. airport and takes the route shown in Figure P3.19. 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 starling point.

Chapter 3, Problem 19P, A commuter airplane starts from ar. airport and takes the route shown in Figure P3.19. The plane

Figure P3.19

Expert Solution & Answer
Check Mark
To determine
 The location and direction of the city from the starting point.

Answer to Problem 19P

Solution:

The location and direction of the city C is 245km and 21.3° West of North respectively.

Explanation of Solution

Given Info:

The magnitude of vector OA is 175km , the magnitude of vector AB is 150km , and the magnitude of vector BC is 190km .

Write the formula to calculate the x-component of OA.

x1=OAcosθ1

  • x1 is the horizontal or x-component of the vector OA
  • OA is the magnitude of the vector OA
  • θ1 is the angle made by the OA vector with respect to the x- axis

Substitute 30.0° for θ1 and 175km for OA to calculate x1 .

x1=(175km)cos(30.0°)=(175km)(0.866)=151.55km

Write the formula to calculate the x-component of AB.

x2=ABcosθ2

  • x2 is the horizontal or x-component of the vector AB
  • AB is the magnitude of the vector AB
  • θ2 is the angle made by the AB vector with respect to the x- axis

Substitute 110.0° for θ2 and 150km for AB to calculate x2 .

x2=(150km)cos(110.0°)=(150km)(0.34)=51.3km

Write the formula to calculate the x-component of BC.

x3=BCcosθ3

  • x3 is the horizontal or x-component of the vector BC
  • BC is the magnitude of the vector BC
  • θ3 is the angle made by the BC vector with respect to the x- axis

Substitute 180.0° for θ3 and 190km for BC to calculate x3 .

x3=(190km)cos(180.0°)=(190km)(1)=190km

Write the formula to calculate the total x component.

x=x1+x2+x3

  • x is the total x component.

Use 151.55km for x1 , 51.3km for x2 and 190km for x3 in the above expression for x.

x=151.55km51.3km190km=89.75km

Write the formula to calculate the y-component of OA.

y1=OAsinθ1

  • y1 is the vertical or y-component of the vector OA
  • θ1 is the angle made by the OA vector with respect to the y- axis

Substitute 30.0° for θ1 and 175km for OA to calculate y1 .

y1=(175km)sin(30.0°)=(175km)(0.5)=87.5km

Write the formula to calculate the y-component of AB.

y2=ABsinθ2

  • x2 is the vertical or y-component of the vector AB
  • θ2 is the angle made by the AB vector with respect to the y- axis

Substitute 110.0° for θ2 and 150km for AB to calculate y2 .

y2=(150km)sin(110.0°)=(150km)(0.94)=140.95km

Write the formula to calculate the y-component of BC.

y3=BCsinθ3

  • y3 is the vertical or y-component of the vector BC
  • θ3 is the angle made by the BC vector with respect to the y- axis

Substitute 180.0° for θ3 and 190km for BC to calculate y3 .

y3=(190km)sin(180.0°)=(190km)(0)=0km

Write the formula to calculate the total y component.

y=y1+y2+y3

  • y is the total y component.

Use 87.5km for y1 , 140.95km for y2 and 0km for y3 in the above expression for y.

y=87.5km+140.95km+0km=228.45km

Write the formula to calculate the location of the city.

r=x2+y2

  • r is the location of the city from the starting point

Substitute 89.75km for x and 228.45km for y to calculate r.

r=(89.75km)2+(228.45km)2=8010.5+52212.5=245.4km245km

Write the formula to calculate the direction of the city.

θ=tan1(|x|y)=tan1(|89.5km|228.5km)=tan1(0.39)=21.3°

Conclusion:

Therefore, the location and direction of the city C is 245km and 21.3° West of North respectively

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A commuter airplane starts from an airport and takes the route shown in Figure P3.17. 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 o west of north y(km) 250 E B W E 200 20.0° b R 150 00 110° a S0.0 x (km) 50 100 150 200 Figure P3.17
A commuter airplane starts from an airport and takes the route shown in Figure P3.19. 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.
A commuter airplane starts from an airport and takes the route shown in Figure P3. 19. 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.

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