Question

Using the diagram shown, what is the magnitude of the resultant of these three forces?

Answer 1

Explanation:

The x component of the resultant force is the sum of the x components of the individual forces.

Fₓ = 65.0 cos 30° − 20.0 sin 20° − 30.0

Fₓ = 19.5

The y component of the resultant force is the sum of the y components of the individual forces.

Fᵧ = 65.0 sin 30° − 20.0 cos 20°

Fᵧ = 13.7

The magnitude is found with Pythagorean theorem:

F² = Fₓ² + Fᵧ²

F² = (19.5)² + (13.7)²

F = 23.8