Answer:
F = 241.8 N θ = -18.7
Explanation:
To find the net force, we use Newton's second law, for this we decompose the force using trigonomer
Force 2
F2 = 61.5 N
cos 45 = F₂ₓ / F2 F₂ₓ = F2 cos 45
sin 45 = F₂_y / F2 F₂_y = F2 sin 45
force 3
F3 = 171 N
cos 45 = F₃ₓ / F3
sin 45 = F₃_y / F3
the total force can be found with its components
axis x direction (East-West)
Fₓ = 64.7 +61.5 cos 45 + 171 cos 45
Fₓ = 229.1 N
Y axis (direction North -Sur)
F_y = 61.5 sin 45 - 171 sin 45
F_y = - 77,428 N
the resulting force is
F = Fx i ^ + Fy j ^
F = (229.1 i⁻ 77,428 j⁾ N
we can use the Pythagorean theorem to find the module
F = √ (229.1 2 + 77,428 2)
F = 241.8 N
let's use trigonometry to find the direction
tan θ = F_y / Fₓ
θ = tan⁻¹ (F_y / Fₓ)
θ = tan⁻¹ (-77,428 / 229.1)
θ = -18.7
