A courier starts from the origin and travels sequentially along three displacement…

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A courier starts from the origin

O

and travels sequentially along three displacement vectors: (i)

\mathbf{d}_1=5\text{ km}

due east, (ii)

\mathbf{d}_2=7\text{ km}

30^{\circ}

north of east in the horizontal plane, (iii)

\mathbf{d}_3=4\text{ km}

due north. Answer the following: (a) Write each displacement in component form using unit vectors

\hat{i}

(east) and

\hat{j}

(north). (b) Find the resultant displacement vector

\mathbf{R}

in unit–vector form. (c) Calculate the magnitude of

\mathbf{R}

. (d) Determine the bearing of

\mathbf{R}

measured as the angle north of east.