Answer:
F = 1494.52 N, θ = 44º
Explanation:
For the sum of vectors by the parallelogram method, see attached, the vectors are drawn, the parallelogram is completed and a vector is drawn from the origin of the two vectors to the end point of the rectangle, this is the resulting vector.
The attachment shows this roughly.
For the Cartesian coordinate method, each vector is decomposed into its components, they are added algebraically and then the resulting vector is composed in the form of a module and angles
we use trigonometry to decompose the vectors.
The coordinate system can be seen in the attachment
sin θ = y / R
cos θ = x / R
y = R sin θ
x = R cos θ
Vector 1
module F₁ and angle β₁ = 50
sin 50 =
cos 50 =
= F₁ sin 50
F₁ₓ = F₁ cos 50
F_{1y} = 600 sin 50 = 459.63 N
F₁ₓ = 600 cos 50 = 385.67 N
Vector 2
modulus F₂ = 900N, angle β₂ = 40
F_{2y} = 900 sin 40 = 578.51 N
F₂ₓ = 900 cos 40 = 689.44 N
we find the resultant of each component
F_{y} =F_{1y} + F_{2y}
F_{y} = 459.63 + 578.51
F_{y} = 1038.14 N
Fₓ = F₁ₓ + F₂ₓ
Fₓ = 385.67 + 689.44
Fₓ = 1075.11 N
We use the Pythagorean theorem to find the modulus of the resultant
F = Fₓ² +
F = √(1075.11² + 1038.14²)
F = 1494.52 N
we use trigonometry for the angle
tan θ = F_y / Fₓ
θ = tan⁻¹ (F_y / Fₓ)
θ = tan⁻¹ (1038.14 / 1075.11)
θ = 44º
