A displacement vector ( A =4

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A displacement vector

\mathbf{A}=4\,\text{km}\;\mathbf{\hat{i}}+3\,\text{km}\;\mathbf{\hat{j}}

is added to another displacement vector

\mathbf{B}

. The resultant

\mathbf{R}=\mathbf{A}+\mathbf{B}

has magnitude

10\,\text{km}

and makes an angle of

60^{\circ}

measured counter-clockwise from the positive

x

-axis. Answer the following parts in sequence. (i) Write separate component equations for the

x

- and

y

-components of the resultant in terms of the unknown components

B_x

and

B_y

. (ii) Using the conditions on magnitude and direction of

\mathbf{R}

, calculate the numerical values of

B_x

and

B_y

. (iii) Hence determine the magnitude and direction (with respect to the

x

-axis) of vector

\mathbf{B}