How did the book get this answer? Please help with motion

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The discussion revolves around a navigation problem involving a ship's displacement and average velocity. The navigator initially records the lighthouse's bearing as N 27 E, but after sailing, the lighthouse is noted to be 15 km due north. The user calculates the horizontal displacement incorrectly, arriving at 8.10 km instead of the correct 9.2 km. Participants suggest that the book may have used a different bearing, specifically N 37 E, which could explain the discrepancy in the answers. The conversation highlights the importance of accurate bearing interpretation in navigation calculations.
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Homework Statement


A ship is 8km from a coastline that stretches in a east west direction. The navigator on the ship records that the lighthouse on the coastline has a bearing of N 27 E. After sailing for 30 minutes the navigator records that the lighthouse is 15km due north.

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

Homework Equations


a^2 + b^2=C^2
v=X/t
v=u+at

The Attempt at a Solution


Horizontal displacement:
x= 8tan27
horizontal displacement = 4.08km

Find displacement via Pythagorus:
x^2 = a^2+b^2
x^2= 4.08^2 + 7^2
Displacement = 8.10 km = WRONG, Right= 9.2km

How is the above answer possible, as I have worked this question out many different ways and still not got this answer.

Could someone please assist me with this problem?

I have attached my freebody diagram (I don't posses very good Paint skills)

Homework Statement


Homework Equations


The Attempt at a Solution

 

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Um, even though you didn't actually state the question, if it's what I think it is, I agree with your answer.
 
Dick said:
Um, even though you didn't actually state the question, if it's what I think it is, I agree with your answer.

Thank you for noticing - I've fixed it now :)

The question was about the ships displacement.
 
TheKovac said:
Thank you for noticing - I've fixed it now :)

The question was about the ships displacement.

Right. Then I definitely agree with your answer.
 
Dick said:
Right. Then I definitely agree with your answer.

Thank you for your answer - I was quite perplexed by their answer, I am glad I am right. :D

Thanks for your help, I really appreciate it! Its great to know that I can get some support with physics, outside of school.

Kindest Regards,
TheKovac
 
… wrong bearing …

Hi everyone!

I think the book was working on a bearing of N 37 E. :frown:
 

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