Question

A force 4N acts along the X- direction. Another force 5N makes an angle

60° with the first force. Find the magnitude and direction of the resultant.

Answer 1

$$R_x=4\ N\cdot cos0^{\circ}+5\ N\cdot cos60^{\circ}=6.5\ N,$$ $$R_y=4\ N\cdot sin0^{\circ}+5\ N\cdot sin60^{\circ}=4.33\ N.$$

The resultant of the sum of two forces can be found from the Pythagorean theorem:

$$R=\sqrt{R_x^2+R_y^2}=\sqrt{(6.5\ N)^2+(4.33\ N)^2}=7.81\ N.$$

We can find the angle as follows:

$$\theta=cos^{-1}(\dfrac{R_x}{R})=cos^{-1}(\dfrac{6.5\ N}{7.81\ N})=33.6^{\circ}.$$

The resultant R has magnitude 7.81 and angle of $33.6^{\circ}$ above the positive x-axis.