Answer:
0.386 m/s² at 187°
Explanation:
According to Newton's second law of motion, the net force (ΣF) on an object is equal to its mass (m) times its acceleration (a). By resolving the forces into x and y components, we can find the components of the acceleration vector. From there, we can use Pythagorean theorem to find the magnitude of the acceleration, and trigonometry to find the direction.
The x component of each force is F cos θ, where F is the magnitude of the force and θ is the direction. The net force in the x direction is therefore:
ΣFₓ = 255 N cos 43.5° + 360 N cos 212°
ΣFₓ = -120.3 N
The y component of each force is F sin θ, where F is the magnitude of the force and θ is the direction. The net force in the y direction is therefore:
ΣFᵧ = 255 N sin 43.5° + 360 N sin 212°
ΣFᵧ = -15.24 N
Using Newton's second law of motion, the components of the acceleration are:
ΣF = ma
a = ΣF / m
aₓ = -120.3 N / 314 kg = -0.383 m/s²
aᵧ = -15.24 N / 314 kg = -0.049 m/s²
Using Pythagorean theorem, the magnitude of the acceleration is:
a² = aₓ² + aᵧ²
a² = (-0.383 m/s²)² + (-0.049 m/s²)²
a = 0.386 m/s²
Using trigonometry, the direction of the acceleration is:
tan θ = aᵧ / aₓ
tan θ = -0.049 m/s² / -0.383 m/s²
θ = 187°
