Mathematics

Problem

Two horizontal forces

\mathbf{F}_1

and

\mathbf{F}_2

act simultaneously on a particle lying on a horizontal plane. Their resultant force is

50\,\text{N}

directed at an angle of

30^{\circ}

above the positive

x

-axis. a. (i) Express the resultant force in unit–vector notation

\hat{i},\hat{j}

. b. (ii) Given that

\mathbf{F}_1=30\,\text{N}

acting vertically upward (along the positive

y

-axis), determine the

x

- and

y

-components of

\mathbf{F}_2

. c. (iii) Hence calculate the magnitude and direction (angle with the positive

x

-axis) of

\mathbf{F}_2

. d. (iv) Verify by direct component addition that

\mathbf{F}_1+\mathbf{F}_2

equals the given resultant.