Ship displacement with lighthouse bearing N27E

[pivoxa15]

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.

 

[hage567]

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.

 

[Mindscrape]

I sure as hell can't get anything out of that problem. How do you know what direction the boat is initially sailing in?

 

[pivoxa15]

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.

 

[denverdoc]

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.

 

[pivoxa15]

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.