Find the magnitudes of (a) vector B and (b) vector C?

Question

The Route followed by a hiker consists of three displacement vectors A,B,and C. Vector A is along a measured trail and is 1770m in a direction 27 degrees north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 43. degrees east of south. Similarly, the direction of Vector C is 32 degrees north of west the hiker ends up back where she started so the resultant displacement is zero, or A+B+C=0

Answer 1

You need to break down each vector into its x and y components.

For vector A, the x component is 1770 cos27=1629; the y component is 1770 sin27 = 803.5

since the hiker returns to the starting points, the sum of the x components of A+B+C=0, and also the sum of the y components of A+B+C=0

the x component of vector B = +Bsin43=0.68 B

the y component of vector B = - Bcos43= - 0.73B

the x component of vector C = -C cos 32 = -0.85C

the y component of vector C= C sin32 = 0.53C

our equations are then:

1629+ 0.68B -0.85C=0

803.5 -0.73B +0.53C=0

this gives you two simultaneous equations to solve for b and c, and you should get that B=5945 and C=6673