Question

Can someone please provide a step by step explanation to the question in the image? It is really important for me to understand these questions. Thanks in advance!​

Answer 1

Answer:

21.21 N @ 81.87°

Explanation:

Divide each force into horizontal components and vertical components.

F₁ is in the +x direction, so F₁ₓ = 12 N and F₁ᵧ = 0 N.

F₂ is in the +y direction, so F₂ₓ = 0 N and F₂ᵧ = 9 N.

F₃ is 53.13° above the -x axis.  So the components are:

F₃ₓ = -15 cos (53.13°) = -9 N

F₃ᵧ = 15 sin (53.13°) = 12 N

The horizontal component of the resultant force is the sum of the horizontal components of the individual forces:

Fₓ = F₁ₓ + F₂ₓ + F₃ₓ

Fₓ = 12 N + 0 N + (-9 N)

Fₓ = 3 N

Similarly, the vertical component of the resultant force is the sum of the vertical components of the individual forces:

Fᵧ = F₁ᵧ + F₂ᵧ + F₃ᵧ

Fᵧ = 0 N + 9 N + 12 N

Fᵧ = 21 N

To find the magnitude of the resultant force, use Pythagorean theorem:

F² = Fₓ² + Fᵧ²

F² = (3 N)² + (21 N)²

F = 21.21 N

To find the direction relative to the +x axis, use trigonometry:

tan θ = Fᵧ / Fₓ

tan θ = (21 N) / (3 N)

θ = 81.87°

The resultant force is 21.21 N at a angle of 81.87° above the +x axis (round as needed).