The route followed by a hiker consists of three displacement vectors A,B, and C.

Question

The route followed by a hiker consists of three displacement vectors A,B, and C. Vector A is along a measure trail and is 1980m in a direction 45.0 degrees north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 44.0 degrees east of south. Similarly, the direction of vector C is 34.0 north of west. the hiker ends up back where she started, so the resultant displacement is zero, or A + B+ C=0. find the magnitudes of vector B and vector C.

Explanation / Answer

only for east direction (positive x axis):

Ax = 1980cos45 = 1400

Bx = Bcos(-46) = 0.69B

Cx = Ccos(180-34) = -0.83C

now 0.69B -0.83C+1400 = 0......................1

similarly only for y axis(north direction):

Ay = 1400

By=-0.72B

Cy = 0.56C

now 1400+0.56C-0.72B = 0.............2

now solving eq 1 and 2 we get

B = 9214m

C=9346.6m

explained in details

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