Forces with magnitude 150 newtons and 220 newtons act on a hook with an angle of 30 degrees. Find the direction and magnitude of the resultant of the forces.

Magnitude of the resultant = 357.85 N

Direction of the resultant is 12.1° from the 220 N force and still in between the two forces 150 N and 220 N

Explanation:

Let the direction in which the 220 N force is acting be the x-axis, then the 150 N force is acting 30° from the 220 N force, i.e. the x-axis.

The 220 N force in vector form = (220cos 0°)î + (220sin 0°)j = (220î) N

The 150 N force in vector form = (150cos 30°)î + (150sin 30°)j = (129.9î + 75j) N

The resultant is the vector sum of both forces = (220î) + (129.9î + 75j) = (349.9î + 75j)

Magnitude = √(349.9² + 75²) = 357.85 N

Direction = tan⁻¹ (75/349.9) = 12.1° From the 220 N force (x-axis)