Ship Displacement & Velocity | 8km to 15km

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Homework Help Overview

The problem involves a ship's displacement and average velocity as it moves from an initial position 8 km from a coastline to a new position 15 km due north, with a specific bearing to a lighthouse. The context is rooted in kinematics and vector analysis.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the accuracy of the original poster's diagram and calculations, questioning the correctness of the provided answer of 9.23 km. Some participants express uncertainty about the initial sailing direction of the ship and whether all values are correctly interpreted.

Discussion Status

The discussion is ongoing, with participants sharing their calculations and interpretations. Some suggest that the book's answer may be incorrect, while others are trying to reconcile their results with the given information. Multiple interpretations of the problem are being explored.

Contextual Notes

There is mention of a potential misinterpretation of the problem, and participants are questioning the validity of the values and assumptions used in their calculations. The original poster's reliance on a diagram and the need for clarity in the problem setup are highlighted.

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Homework Statement


A ship is 8km from a coast-line that stretches in an east-west direction. The navigator on the shop records that the lighthouse on the coast-line has a bearing of N27E. After sailing for 30 minutes the navigator records that the same lighthouse is 15km due north.

a) What is the displacement of the ship between the two recordings?
b) What is the average velocity of the ship?

Homework Equations


The Attempt at a Solution


I have attached a diagram. Is it correct?

If you do calculations from the diagram, you find that the original position was (0,8) and the new position is (4.08,15). So the displacement of the two recordings is (4.08,15)-(0,8)=(4.08,7). Which come down to an absolute length of 8.1km but the answers gave 9.23km as the absolute length. Where have I gone wrong. I can't do b) without knowing how to do a).

If I assume the hypotenues distance as 8km (in the triangle of 27 degrees) than I end up with (3.6,15)-(0,7.13)=(3.6,7.87) which gives an absolute length of 8.7km, which is still not right.
 

Attachments

  • COAST-LINE.GIF
    COAST-LINE.GIF
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Are you sure 9.23 km is supposed to be the right answer? Are you sure you have all the values posted in your question correct? I think your answers are correct for each case based on the info you've given, if the problem is being interpreted correctly.
 
I sure as hell can't get anything out of that problem. How do you know what direction the boat is initially sailing in?
 
hage567 said:
Are you sure 9.23 km is supposed to be the right answer? Are you sure you have all the values posted in your question correct? I think your answers are correct for each case based on the info you've given, if the problem is being interpreted correctly.

That answer was posted at the back of the book. There is a small chance it's wrong. Maybe intepretation is an issue. But I can't intepret it in a way to get the answer they are looking for.
 
I get a displacement of 8.1 using law of cosines where a=8/cos(27), b=15, and theta=27. I say book is wrong.
 
denverdoc said:
I get a displacement of 8.1 using law of cosines where a=8/cos(27), b=15, and theta=27. I say book is wrong.

That's what I got as well so I agree with you.
 

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