Solving Vector Direction & Distance Problems - Guam Example

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Homework Help Overview

The problem involves a ship leaving Guam and sailing at a specified angle and distance, with the goal of determining the direction and distance needed for the ship to achieve a resultant displacement directly east of Guam. The subject area includes vector direction and distance in the context of navigation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for a right triangle to solve the problem and question whether this is the only approach. Some suggest using the Law of Sines and Law of Cosines as alternatives. There is also mention of drawing diagrams to visualize the problem.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some have provided guidance on using trigonometric laws, while others are still seeking clarity on how to proceed with their diagrams and calculations.

Contextual Notes

Participants express uncertainty about the necessity of right triangles and the appropriate trigonometric laws to apply. There is a focus on understanding the relationships between angles and sides in the context of the problem.

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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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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?
 
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.
 
SteamKing said:
How do you know you need a right triangle to figure out the solution?
I don't know what else to use.
 
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.
 
Lefty9602 said:
I drew the problem
Post the figure you drew for the information given.
 
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.
 
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.
 

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