Question icon
Grade 12th passMechanics

While following a treasure map,you start at an old oak tree,you first walk 825m directly south,then turn and walk 1.25km at 30.0degree west north,and finallay walk 1.00km at 40degree north of east,where you find the treasure:a biography of isaac newton.
(a)to return to the old oak tree,in what direction should you head and how far will you walk?use the components to solve this problem.
(b)to see whether your calculation in part (a) is reasonable,check it with a graphical solution drawn roughly to scale.

Profile image of Salim ghali salis
7 Years agoGrade 12th pass
Answers icon

1 Answer

Profile image of Arun
7 Years ago
convert these relative directions.... because 0 is due east on the unit circle, I am going to orient myself relative to due east. 
east = 0 
north = 90 
west = 180 
south = 270 
30 degrees west of north = 120 degrees 
40 degrees east of north = 50 degrees 


825m ( cos 270 , sin 270 ) + 1250m (cos 120, sin 120) + 1000 (cos 50, sin 50) 
(0, -825) + (-625, 1083) + (766, 643) 
(141,900) 
1) what direction should you head to get back to the oak tree... 
atan(900/141) = 81 degrees = (9 degrees east of north) 
this is the direction from the tree to you. To get back to the oak tree you must go the opposite direction. 

261 degrees = 9 degrees west of south. 

what distance? 
900^2 + 141^2 = d^2 = sqrt (830468) = 911 m