Two forces act simultaneously on a small object lying on a smooth horizontal surface

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

Problem

Two forces act simultaneously on a small object lying on a smooth horizontal surface. The forces are

\mathbf{F}_1 = 5\hat{i} - 3\hat{j}\,\text{N}

and

\mathbf{F}_2 = -2\hat{i} + 4\hat{j}\,\text{N}

. (i) Obtain the rectangular components of the net force

\mathbf{F}

acting on the object. (ii) Calculate the magnitude of

\mathbf{F}

. (iii) Find the direction of

\mathbf{F}

measured anticlockwise from the positive

x

-axis. Express your answer in radians correct to two decimal places.