Two forces and act at a point in a horizontal plane

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Two forces

\vec{F_1}

and

\vec{F_2}

act at a point

O

in a horizontal plane.

\vec{F_1}

has magnitude

50\,\text{N}

and is directed along the positive

x

-axis.

\vec{F_2}

has magnitude

80\,\text{N}

and is inclined at

60^{\circ}

to the positive

x

-axis, measured towards the positive

y

-axis. (i) Express

\vec{F_1}

and

\vec{F_2}

in terms of the unit vectors

\mathbf{i}

and

\mathbf{j}

. (ii) Determine the resultant force

\vec{R}=\vec{F_1}+\vec{F_2}

in component form. (iii) Find the magnitude of

\vec{R}

and the angle it makes with the positive

x

-axis, correct to one decimal place.