How Do You Return to the Oak Tree After Finding the Treasure?

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To return to the oak tree after finding the treasure, the correct calculations involve understanding the angles associated with the directions traveled. The initial calculations mistakenly used 50 degrees instead of the correct 40 degrees for the last leg of the journey. The proper angle for the third leg should be considered as 40 degrees north of east, which translates to 50 degrees east of north. The resulting vector calculations yield a distance of approximately 911 m at an angle of 8.9 degrees west of south, which differs from the initial incorrect answer. Clarification on angle measurement is crucial for accurate navigation back to the starting point.
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Homework Statement


While following a treasure map, you start at an old oak tree. You first walk 825 m directly south, then turn and walk 1.25 km at 30degrees west of north, then 1.00 km 40.0 degrees north of east where you find a treasure. To return to the oak tree, in what direction would you walk and how far?


Homework Equations





The Attempt at a Solution


I thought that I did everything right, but can't seem to get the answer that they have in the back of the book. Any help would be appreciated.

R=A+B+C.
A = 270 degrees B= 120 degrees C = 50 degrees

Ax = Acos\Theta= (825m)(cos 270) = 0
Ay = Asin \Theta= (825)(sin270) =-825m
Bx= (1250m)(cos 120) = -625m
By= (1250) (sin 120) = 1082.53m
Cx=(1000)(cos50) = 642.78m
Cy=(1000)(cos 50) = 766m

Rx= 17.78m Ry = 1023.53 R= \sqrt{}(17.78^2)+(1023.53^2) = 1023.68m

arctan (1023.53/17.78) = 89 degrees

The answer I come up with is 1023.7 m at 1 degree west of south.

The answer in the book is 911 m at 8.9 degrees w of s.

Thanks for the help!
 
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Your third angle should be 40 not 50... is use cos40 not cos50 etc...
 
learningphysics said:
Your third angle should be 40 not 50... is use cos40 not cos50 etc...

Forgive me, but could you explain why. Perhaps I am not understanding the angle calculation, but I thought it was counterclockwise from the + x-axis towards the + y-axis and I thought that with it being 40 degrees north of east, it would be 90-40. I am sorry if this sounds like a stupid question, but I am trying to understand where I am going wrong so that I can understand what to do the next time...

Thank you :)

Amy
 
eeriana said:
Forgive me, but could you explain why. Perhaps I am not understanding the angle calculation, but I thought it was counterclockwise from the + x-axis towards the + y-axis and I thought that with it being 40 degrees north of east, it would be 90-40. I am sorry if this sounds like a stupid question, but I am trying to understand where I am going wrong so that I can understand what to do the next time...

Thank you :)

Amy

If you go counterclockwise from the +x axis towards the y-axis... that's the same as going north of east... The angle east of north is 50... the angle north of east is 40.

going north from east... is the same as going counterclockwise towards the y-axis... because you are going up from the positive x-axis...
 
Last edited:
learningphysics said:
If you go counterclockwise from the +x axis towards the y-axis... that's the same as going north of east... The angle east of north is 50... the angle north of east is 40.

going north from east... is the same as going counterclockwise towards the y-axis... because you are going up from the positive x-axis...

I think I see what you're saying.

Thank you for your help...

Amy
 
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