Why Do My Calculations for Ship Positions Differ from the Textbook Answers?

[delcypher]

Hi this seems like a simple question (and probably is) but I keep getting the answers wrong.

Homework Statement

Two ships, A and B, leave port P at the same time. Ship A travels due north at a steady speed of 15kmh$$^{-1}$$ and ship B travels N 60$$^{o}$$ E at a speed of 10kmh$$^{-1}$$.

i) What is the distance and direction from A to B after 1 hour?
ii) What is the velocity of B relative to A?

Homework Equations

c$$^{2}$$ = a$$^{2}$$ + $$^{2}$$ - 2.a.b.COSC

COS 60$$^{o}$$ = 0.5; SIN 30$$^{o}$$ = 0.5; cos 30$$^{o}$$ = ($$\sqrt{3}$$)/2

The Attempt at a Solution

The workings can be seen here (sorry I prefer to write):
http://www.unicyclist.com/gallery2/main.php?g2_view=core.DownloadItem&g2_itemId=551574&g2_serialNumber=1"

The answer given in the book for the distance between A and B in i) should be 13.33Km, my calculations make it 13.23Km, it's close but not enough for me to be certain I've done it correctly.

The direction for i) is correct they've (in my opinion) written it a strange way.

I wrote 139.11$$^{o}$$ (from North clockwise) or E 49.11$$^{o}$$ S. They wrote S 40$$^{o}$$ 54' E - this means S 40.9$$^{o}$$ E

My answer for ii) is very close 13.23kmh$$^{-1}$$, but they give 13.22kmh$$^{-1}$$.

Can anyone shed any light on what I'm doing wrong?

 

[Doc Al]

Looks good to me. Your answers are correct.

 

[delcypher]

Would you say then that the book's answers are incorrect?

Maybe they've used a different method and rounded with the cos30 rather than using it's surd value?

 

[Doc Al]

I agree with your answers; where the book disagrees, the book is incorrect. Beats me why--but it does happen.

 

[delcypher]

okay, thank-you for taking the time to look at my messy workings.