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

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 25.0° 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° east of south. Similarly, the direction of vector vector C is 20.0° 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

Length of A is 1550 m.

Let length of vector B be B and vector C be C

Since net displacement is 0. It should be 0 along bith X and Y axis

Sum of Componet of all displacement along X axis is:

1550*cos(25) + B*sin(41) - C*cos(20) = 0

1404.3 + 0.656*B - 0.940*C =0 ... eqn 1

Sum of Componet of all displacement along Y axis is:

1550*sin(25) - B*cos(41) + C*sin(20) = 0

655.65 - 0.755*B + 0.342*C= 0 .... eqn 2

solve eqn 1 and eqn 2

And get B , C

Magnitude of B = m

Magnitude of C = m

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