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 measured trail and is 1550 m in a direction 21.0 degree north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0 degree east of south. Similarly, the direction of vector C is 27.0 degree 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. magnitude of B m magnitude of C m

Explanation / Answer

The angles are (where a=angle opposite vector A etc) b = 21+ 35= 56 deg c = 41+(90-27) = 104 deg a = 180-b-c = 20 deg Magnitude of vector B = 1550*sin(56)/sin(20) = 3757.1m Magnitude of vector C = 1550*sin(104)/sin(22) = 4397.28 m

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