The acceleration vector that results from the forces is 1.51 m/s² 18.9⁰ east of north. (Option B).
How to calculate the acceleration vector?
The acceleration vector that results from the forces is calculated by applying the following formula as shown below;
The sum of the forces in x - direction;
Fx = 145 N - 120 N x cos (30)
Fx = 41.08 N
The sum of the forces in y - direction;
Fy = 60 N + 120 N x sin (30)
Fy = 120 N
The resultant force is calculated as follows;
F = √ (Fx² + Fy²)
F = √ (41.08² + 120²)
F = 126.84 N
The direction of the resultant force is calculated as;
tan θ = Fy / Fx
tan θ = 120 / 41.08
tan θ = 2.921
θ = arc tan (2.921)
θ = 71.1 ⁰
The direction in east = 90 - 71.1 ⁰
θ = 18.9⁰
The acceleration of the object is calculated as;
a = F(net) / m
a = (126.84 N) / 84.1 kg
a = 1.51 m/s²