Final answer:
The magnitude of the resulting acceleration is approximately 14.52 m/s^2.
Step-by-step explanation:
To find the magnitude of the resulting acceleration, we need to consider the forces acting on the block. In this case, we have two forces: one in the east direction and the other in the north direction. The magnitude of each force is 277 N. We can treat them as vectors and use vector addition to find the resulting force.
To find the resulting force, we can use the Pythagorean Theorem. The magnitude of the resulting force is given by the equation F_resultant = sqrt(F_east^2 + F_north^2), where F_east is the eastward force and F_north is the northward force. Plugging in the values, we get F_resultant = sqrt((277 N)^2 + (277 N)^2) = 391.96 N.
Next, we can use Newton's second law to find the acceleration of the block. The equation is F_resultant = mass * acceleration. Rearranging the equation to solve for acceleration, we get acceleration = F_resultant / mass. Plugging in the values, we get acceleration = 391.96 N / 27 kg = 14.52 m/s^2. Therefore, the magnitude of the resulting acceleration is approximately 14.52 m/s^2.