Question

The route followed by a hiker consists of three displacement vectors A with arrow, B with arrow, and C with arrow. Vector A with arrow is along a measured trail and is 1550 m in a direction 23.0° north of east. Vector B with arrow 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 40.0° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A with arrow + B with arrow + C with arrow = 0. Find the magnitudes of vector B with arrow and vector C with arrow.

Answer 1

If the sum of three vectors is zero then the individual sums of their x and y components will also be zero.

Therefore

by plugging all the values we get

eq-1

and

or

eq-2

There are two equations with two variables B and C

by solving both the equations we get