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 2040 m in a direction 19.0 ° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 26.0 ° east of south. Similarly, the direction of vector C is 42.0 ° 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 (a) vector B and (b) vector C.

A)
B)

Explanation / Answer

Solve this by using component system
measure all angles from due east
then A is at 19.0 degree
B is at -64 degree
C is at 138 degree

now A = Acos(19)x + Asin(19)y            [A is the magnitude of A and so on]
B = Bcos(-64)x + Bsin(-64)y
C = Ccos(138)x + Csin(138)y

Since the summation is zero, individual components must also sum to 0

Acos(19) + Bcos(-64) + Ccos(138) = 0

Asin(19) + Bsin(-64) + Csin(138) = 0

Substitute all the knowns (A, and all the sines and cosines) and u'll get a simple linear equation in 2 variables, which you can easily solve for B and C :-)

Msg if you need more help...

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