Physics

Problem

A particle starts from the origin and undergoes three successive displacements in the

x

–

y

plane:

\mathbf{S}_1=3\,\mathbf{\hat{i}}+4\,\mathbf{\hat{j}}\;\text{m}

\mathbf{S}_2=-5\,\mathbf{\hat{i}}+2\,\mathbf{\hat{j}}\;\text{m}

, and

\mathbf{S}_3=4\,\mathbf{\hat{i}}-6\,\mathbf{\hat{j}}\;\text{m}

. a. (i) Find the resultant displacement vector

\mathbf{R}

of the particle. b. (ii) Calculate the magnitude of

\mathbf{R}

. c. (iii) Determine the unit vector

\mathbf{\hat{r}}

along

\mathbf{R}

. d. (iv) If the particle now travels

10\,\text{m}

in the direction opposite to

\mathbf{R}

, obtain its final coordinates.