You are on a treasure hunt and your map says "Walk due west for 52 paces, then walk 29.6° north of west for 40 paces, and finally walk due north for 25 paces." What is the magnitude of the component of your displacement in the following directions?

Question

(a) due north
paces

(b) due west
paces

Answer 1

Label starting point (0,0)

after walking due west, you are at (-52,0)

From there, your next displacement is (40 cos 150.4° , 40 sin 150.4°) = (-34.78,7.22), and you are now at (-86.78,7.22)

From there, you now displace (0,25) and end up at (-86.78,32.22)

Answer 2

Another Method:

D = -52 + 40[150.4] + 25i
D = -52 + -34.8 + 19.8i + 25i
D = -86.8 + 44.8i, Q2.

D = (X,Y) = (-86.8, 44.8).