Solve Hard Vector Problem: Location of City C

In summary, the conversation is about finding the location of city C relative to the starting point after a commuter airplane flies to city A, then to city B, and finally to city C. The solution involves finding the x and y components of each vector and using them to find the displacement components, which are then used to find the distance and angle of city C. There were some errors in the attempt at a solution, including the incorrect angle for vector B and confusion between magnitude and angle.
  • #1
mandy9008
127
1

Homework 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.


Homework Equations





The Attempt at a Solution


I found the X and Y components of each vector (A, B, and C) and then added them to find the D components, which i then solved for D, the distance
Ax=175 cos 30 = 151.6
Ay=175 sin 30 = 87.5
Bx=150 cos 20 =140.9
By=150 sin 20 = 51.3
Cx=190 cos 180 = -190
Cy=190 sin 180 = 0

Dx=102.5
Dy=138.8

D=square root (138.8/102.5)
D=1.16
 
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  • #2


mandy9008 said:

Homework 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.


Homework Equations





The Attempt at a Solution


I found the X and Y components of each vector (A, B, and C) and then added them to find the D components, which i then solved for D, the distance
Did you draw a picture?
mandy9008 said:
Ax=175 cos 30 = 151.6
Ay=175 sin 30 = 87.5
These are correct for the coordinates of city A.
mandy9008 said:
Bx=150 cos 20 =140.9
By=150 sin 20 = 51.3
These aren't correct, nor are the coordinates for city C. City A isn't at the origin, so you have to take the coordinates of A into account when you find the coordinates of city B.
mandy9008 said:
Cx=190 cos 180 = -190
Cy=190 sin 180 = 0

Dx=102.5
Dy=138.8

D=square root (138.8/102.5)
Where did you get this formula?
mandy9008 said:
D=1.16
 
  • #3


Mark44, it looks like Bx and By are not meant to be the coordinates of city B, rather they are the displacement components from A to B.

mandy9008, there are a couple of errors in your work. First, the angle for vector B is not 20°. You need to figure out the angle with respect to due east.

Also, you seem to be confusing the magnitude of a vector with the angle of the vector here:
mandy9008 said:
Dx=102.5
Dy=138.8

D=square root (138.8/102.5)
D=1.16
Please look up the formulas for magnitude and angle of a vector in terms of its x and y components.
 

FAQ: Solve Hard Vector Problem: Location of City C

How do I approach solving a hard vector problem?

To solve a hard vector problem, start by identifying the known and unknown variables, and the given information. Then, use vector addition and subtraction to create a system of equations that can be solved algebraically. It may also be helpful to draw a diagram to visualize the problem.

What is the importance of the location of City C in a vector problem?

The location of City C serves as a reference point for the other cities in the problem. It helps to determine the direction and magnitude of the vectors in relation to City C. Without knowing the location of City C, it would be difficult to accurately solve the vector problem.

Can I use trigonometry to solve vector problems?

Yes, trigonometry can be used to solve vector problems, particularly when dealing with angles and direction. The sine, cosine, and tangent functions can be used to find the components of vectors and to find the resultant vector.

How can I check if my answer to a vector problem is correct?

To check if your answer is correct, you can use the Pythagorean theorem to calculate the magnitude of the resultant vector. You can also use the angle between the resultant vector and the x-axis to verify the direction of the vector.

Are there any tips for solving vector problems more efficiently?

One tip for solving vector problems more efficiently is to break down complex vectors into smaller components. This can make the problem more manageable and easier to solve. Additionally, double-checking your calculations and using a calculator with vector functions can help to reduce errors and save time.

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