Physics

Problem

Suppose a displacement vector

\mathbf{p}

has magnitude

7\,\text{km}

and makes an angle of

30^{\circ}

north of east with the positive

x

-axis. Another displacement vector

\mathbf{q}

has magnitude

5\,\text{km}

and makes an angle of

60^{\circ}

south of east. Answer the following: a. (i) On graph paper, choose a convenient scale (for example,

1\,\text{cm}=1\,\text{km}

). Draw

\mathbf{p}

with its tail at the origin. By an appropriate construction, draw the vector

\mathbf{r}

which, when added to

\mathbf{p}

, will carry the particle to the tip of

\mathbf{q}

. Label all vectors clearly. b. (ii) Measure and record the magnitude and direction of

\mathbf{r}

correct to one decimal place and to the nearest degree respectively. c. (iii) Resolve

\mathbf{p}

and

\mathbf{q}

into rectangular components, calculate

\mathbf{r}

analytically and compare your numerical result with the measurements obtained in part (ii).