Answer:
187.22°
Explanation:
According to Newton's second law of motion, the net force on an object is equal to the mass times the acceleration. By resolving the forces into their x and y components, the components of the acceleration vector can be found. We can then use trigonometry to find the direction.
The x and y components of a force are Fₓ = F cos θ and Fᵧ = F sin θ.
The x component of the first force is:
F₁ₓ = F₁ cos θ₁
F₁ₓ = 255 cos 43.5
F₁ₓ = 184.97 N
The y component of the first force is:
F₁ᵧ = F₁ sin θ₁
F₁ᵧ = 255 sin 43.5
F₁ᵧ = 175.53 N
The x component of the second force is:
F₂ₓ = F₂ cos θ₂
F₂ₓ = 360 cos 212
F₂ₓ = -305.30 N
The y component of the second force is:
F₂ᵧ = F₂ sin θ₂
F₂ᵧ = 360 sin 212
F₂ᵧ = -190.77 N
The x component of the acceleration is:
∑Fₓ = maₓ
F₁ₓ + F₂ₓ = maₓ
184.97 + -305.30 = 314 aₓ
aₓ = -0.3832 m/s²
The y component of the acceleration is:
∑Fᵧ = maᵧ
F₁ᵧ + F₂ᵧ = maᵧ
175.53 + -190.77 = 314 aᵧ
aᵧ = -0.0485 m/s²
Using trigonometry, the angle of the acceleration vector relative to the +x axis is:
tan θ = aᵧ / aₓ
tan θ = -0.0485 / -0.3832
tan θ = 0.1267
θ = 187.22°
