A surveyor walks along three successive displacement vectors in the following order: 1
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A surveyor walks along three successive displacement vectors in the following order:
1. S1: 150\,m at 40∘ north of east
2. S2: 200\,m due south
3. S3: unknown
At the end of the third displacement the surveyor finds herself exactly at the starting point.
(a) Write the components of S1 and S2 on an x-y coordinate system with east as +x and north as +y.
(b) Using the fact that the algebraic sum of the three displacement vectors is the zero vector, obtain the x- and y-components of the unknown displacement S3.
(c) Determine the magnitude of S3.
(d) Find the direction of S3 expressed as an angle measured south of west or north of west, whichever is smaller.
(e) Sketch, to scale, the closed triangle of displacements and label all vectors clearly to demonstrate that the three vectors indeed form a closed triangle.