Halliday, Resnick & Walker — Vectors: Problem 55

A particle undergoes three successive displacements in a plane, as follows: \(\vec{d}_1\), 4.00 m southwest; then \(\vec{d}_2\), 5.00 m east; and finally \(\vec{d}_3\), 6.00 m in a direction 60.0° north of east. Choose a coordinate system with the \(y\) axis pointing north and the \(x\) axis pointing east. What are (a) the \(x\) component and (b) the \(y$ component of \(\vec{d}_1\)? What are (c) the \(x\) component and (d) the \(y\) component of \(\vec{d}_2\)? What are (e) the \(x\) component and (f) the \(y\) component of \(\vec{d}_3\)? Next, consider the net displacement of the particle for the three successive displacements. What are (g) the \(x\) component, (h) the \(y\) component, (i) the magnitude, and (j) the direction of the net displacement? If the particle is to return directly to the starting point, (k) how far and (l) in what direction should it move?