Ship Displacement & Velocity | 8km to 15km

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The discussion centers on calculating the displacement and average velocity of a ship based on its recorded positions relative to a lighthouse. The initial position is noted as (0,8) and the new position as (4.08,15), leading to a calculated displacement of (4.08,7) with an absolute length of 8.1 km. However, there is confusion regarding a provided answer of 9.23 km, with participants questioning the accuracy of the book's solution and the interpretation of the problem. Various calculations using the law of cosines yield similar results, reinforcing doubts about the correctness of the book's answer. The consensus is that the problem may be misinterpreted or that the book contains an error.
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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.
 

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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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