Know Your Bearings

SydneyRoverP6B

SydneyRoverP6B

Well-Known Member
Staff member
Two ships sail from Nantucket at the same time. Essex sails 21 nautical miles due east in three hours, whilst the other vessel the Pequod sails 30 nautical miles in the same time on a bearing of 163 degrees. At this time how far apart are the two vessels?

Ron.

P.S This is my 1000th post too... :D
 
cool. I love these puzzles:) i have a time limit this time too as we're off to crete on tuesday....

Rich.
 
OK, I'm no mariner, but I'm making these assumptions (and please tell me if they are wrong!)

North = 0 deg, East = 90 deg, South = 180 deg, West = 270 deg.

In vectors terms...

Essex position = 21i and Pequod = 30 @ (163-90) deg = 30 @ 73 deg = 8.771151 i - 28.689143 j

From the Essex to Pequod, we go from Essex to origin, and from origin to Pequod, so, (-21i) + (8.771151 i - 28.689143) j

Eseex to Pequod = -12.228849 i - 28.689143 j = 31.187 nautical miles

I get the straight line distance between them to be 31.187 nautical miles.

And I see quattro has stolen my thunder again! :p
 
Hello Rich, Richard and Darth,

Glad you liked the problem,...a nice easy one to start the day... :D

Rich,..do you agree with your fellow mathematicians?

I have another one which you might like to put your mind to...I'll post it now.

See what you think... :p

Ron.
 
I used the cosine rule c2=a2+b2-2(a)(b)(cosC)

So c2 = 900+441-(2x30x21x0.2924)

= 1341-368.424

= 972.576

C = 31.186

Sorry Darth, I'll email your thunder back 8)
 
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