Solving Vector Direction & Distance Problems - Guam Example

In summary: The angle you get is measured south of east from that point. Basically, it's asking for the angle of the path expressed relative to a line directly east. The angle you get is measured south of east from that point.
  • #1
Lefty9602
4
0

Homework Statement


A ship leaves the island of Guam and sails a distance 300km at an angle 46.0∘ north of west.

In which direction must it now head so that its resultant displacement will be 115km directly east of Guam? (Express your answer as an angle measured south of east)
part B:
How far must it sail so that its resultant displacement will be 115km directly east of Guam?

Homework Equations

The Attempt at a Solution


I drew the problem out and tried to find a right triangle but I can't seem to get one to solve these problems. What do I need to do?
 
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  • #2
Lefty9602 said:

Homework Statement


A ship leaves the island of Guam and sails a distance 300km at an angle 46.0∘ north of west.

In which direction must it now head so that its resultant displacement will be 115km directly east of Guam? (Express your answer as an angle measured south of east)
part B:
How far must it sail so that its resultant displacement will be 115km directly east of Guam?

Homework Equations

The Attempt at a Solution


I drew the problem out and tried to find a right triangle but I can't seem to get one to solve these problems. What do I need to do?
How do you know you need a right triangle to figure out the solution?
 
  • #3
In your triangle, you know two of the sides and you know the angle between them. This completely specifies the shape of the triangle and you should be able to find any angles by using the laws of sine and cosine. Try to relate the angles of the triangle with the angles that you are looking for.
 
  • #4
SteamKing said:
How do you know you need a right triangle to figure out the solution?
I don't know what else to use.
 
  • #5
Lefty9602 said:
I don't know what else to use.
There are other kinds of triangles besides right triangles.

Do you know the Law of Sines? The Law of Cosines?

One or both of these may be useful in solving your problem, but you won't know if you stay stuck on trying to use right triangles only.
 
  • #6
Lefty9602 said:
I drew the problem
Post the figure you drew for the information given.
 
  • #7
NascentOxygen said:
Post the figure you drew for the information given.
Got everything with law of cosines. I got the angle 11.79 to get to 115 meters east of guahm but I don't know how to make it in the south of east direction.
 
  • #8
Lefty9602 said:
in the south of east direction
Basically, it's asking for the angle of the path expressed relative to a line directly east.
 

1. What are vector direction and distance problems?

Vector direction and distance problems involve finding the direction and magnitude of a vector, which is a quantity that has both magnitude (size) and direction. These problems typically require using trigonometry and geometry concepts to calculate the vector's direction and distance.

2. How do you solve vector direction and distance problems?

To solve vector direction and distance problems, you first need to identify the given information, such as the initial and final positions of the vector. Then, use trigonometric functions, such as sine, cosine, and tangent, to calculate the angle and distance between the initial and final positions. Finally, use the Pythagorean theorem to find the magnitude (distance) of the vector.

3. What is the Guam Example for solving vector direction and distance problems?

The Guam Example is a commonly used example to illustrate how to solve vector direction and distance problems. It involves finding the direction and distance of a plane flying from one location to another on the island of Guam. The problem typically provides the initial and final positions of the plane, as well as the angle and distance between them.

4. What are some tips for solving vector direction and distance problems?

Some tips for solving vector direction and distance problems include drawing a diagram to visualize the problem, labeling the given information, using the appropriate trigonometric functions, and checking your solution for reasonableness. It can also be helpful to break down the problem into smaller, more manageable steps.

5. Why are vector direction and distance problems important in science?

Vector direction and distance problems are important in science because they allow us to describe and analyze the motion of objects in a two-dimensional or three-dimensional space. These problems are commonly used in physics, engineering, and other scientific fields to model and predict the movement of objects, such as airplanes, satellites, and projectiles.

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