Question

The route followed by a hiker consists of three displacement vectors  ,  , and  . Vector  is along a measured trail and is 1490 m in a direction 18.0 ° north of east. Vector  is not along a measured trail, but the hiker uses a compass and knows that the direction is 39.0 ° east of south. Similarly, the direction of vector  is 23.0 ° 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  .

Answer 1

If we simplify the problem there are two unknowns namely the magnitudes of vector a and vector b

And the sum of the given three vectors is zero. We can easily solve the problem by resolving the vectors into their components along two perpendicular directions.

For the detailed solution please find the attached image below