To determine the magnitude of the resulting acceleration of the block, we need to resolve the forces acting on the block into their horizontal and vertical components.
The force of 27 N acts horizontally, so its horizontal component is 27 N.
The force of 81 N acting at an angle needs to be resolved into its horizontal and vertical components. The horizontal component is given by 81 N * cosθ, where θ is the angle between the force and the horizontal direction. Since the angle is not specified in the question, we cannot determine the exact value of the horizontal component without that information.
Once we have the horizontal components of the forces, we can calculate the net horizontal force acting on the block by summing up all the horizontal components. In this case, the only horizontal force is the force of 27 N, so the net horizontal force is 27 N.
Using Newton's second law, F = ma, where F is the net force and m is the mass of the block, we can solve for the acceleration.
a = F / m
a = 27 N / 2.2 kg
a ≈ 12.27 m/s^2
Therefore, the magnitude of the resulting acceleration of the block is approximately 12.27 m/s^2.