What are the displacement vectors and directions of a hiker's route?

[roshanak_fe]

Someone please help me with this problem!

I can't solve problem this problem. I know it's probably very easy to solve, but I don't know why I'm stuck. Please help me break it down...thank you.

The route followed by a hiker consists of three displacement vectors A, B and C. Vector A is along a measured trail and is 3100 m in a direction 20.9° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 43.5° east of south. Similarly, the direction of vector C is 34.9° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A + B + C = 0. Calculate the magnitude of vector B.

 

[TimNguyen]

Break all 3 vectors into x and y components. You could do this because you have the magnitude and direction of the vectors A and C.

 

[ganstaman]

Actually, I don't see a magnitude for vector C, but I also don't think it should be necessary. At least I hope not.

So I would also agree that each vector should be viewed in x and y (or North/South and East/West) coordinates. Since we end up where we started, all northward movement must be countered by an indentical amount of southward displacement (and similarly for east and west).

And don't forget, since you have the angles for each vector, you can easily relate their north/south magnitudes with their east/west ones. Also don't forget to draw a picture of this situation, as it really will make the problem just a bit clearer.