The route followed by a hiker consists of three displacement vectors , , and . V

Question

The route followed by a hiker consists of three displacement vectors , , and . Vector is along a measured trail and is 1160 m in a direction 36.0 degree north of east. Vector is not along a measured trail, but the hiker uses a compass and knows that the direction is 32.0 degree east of south. Similarly, the direction of vector is 31.0 degree north of west. The hiker ends up back where she started, so the resultant displacement is zero, or + + = 0. Find the magnitudes of (a) vector and (b) vector .

Explanation / Answer

sum distances in the x

1160*cos(36) + A*sin(32)-B*cos(31) = 0

so B = (1160*cos(36) + A*sin(32))/cos(31)

sum in the y

1160+sin(36) -A*cos(32) + B*sin(31) = 0

plug in for B

1160+sin(36) -A*cos(32) + (1160*cos(36) + A*sin(32))/cos(31)*sin(31) = 0

solve for A

A=3255.9 m

then B = (1160*cos(36) + 3255.9*sin(32))/cos(31)=3107.7 m

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