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 2730 m in a direction 40.0 degree north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 27.0 degree east of south. Similarly, the direction of vector C is 33.0 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 (a) vector B and (b) vector C. (a) Number Units (b) Number Units

Explanation / Answer

Vector A = 2730 cos 40 i + 2730 sin 40 j

               = 2091.30 i + 1754.81 j

Vector B = B sin 27 i + B cos 27 * -j

               = 0.4539 B i -0.8910 j

Vector C = C cos 33 * -i + C sin 33 j

               = -0.8367 C i + 0.5446 C j

A+B+C = 0

2091.30 i + 1754.81 j + 0.4539 B i -0.8910 j   -0.8367 C i + 0.5446 C j = 0

2091.30 +0.4539 B -0.8367 C = 0 ------------( 1)

1754.81 -0.8910B + 0.5446 C = 0 -----------(2)

Solve the system and find the values

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