Resultant Acceleration of an Object Under Perpendicular Forces

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To find the resultant acceleration of a 40kg object under two perpendicular forces of 45 N and 40 N, the correct approach involves using the Pythagorean theorem. The individual accelerations in the x and y directions are calculated as ax = 1.23 m/s² and ay = 1.23 m/s², leading to a resultant acceleration of approximately 1.74 m/s². However, the initial calculation of 1.2 m/s² aligns with one of the provided answer choices, indicating a potential misunderstanding of the problem. The discussion emphasizes that the angle of the forces does not affect the magnitude of acceleration due to the perpendicular nature of the forces. Clarification on the use of Pythagorean theorem is provided, reinforcing the importance of proper problem-solving techniques in physics.
Jamotron
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A simple problem from a list of many I was working through as revision:

Homework Statement


Two ropes are attached to a 40kg object. The first rope applies a force of 45 N, and the seond 40 N. If the two ropes are perpendicular to each other, what is the resultant acceleration?
a)1.2m/s2
b)3.0m/s2
c)25m/s2
d)47m/s2

Homework Equations


F=ma
F1x=F1cos theta1
F2x=F2cos theta2

F1y=F1sin theta1
F2y=F2sin theta2

a=(ax2+ay2)1/2

The Attempt at a Solution


As the angles of ropes to the object are not given but the ropes are stated as being perpendicular I took 45 degrees as the angle of both ropes, which gives me the same answer for Fx and Fy which is49.45N. Therefore:
ax=Fx/M = 1.23m/s2
ay=Fy/M=1.23m/s2
Now, this value is consistent with answer a) given in the question. However I was under the impression that to find the magnitude of the acceleration I need to use the equation
a=(ax2+ay2)1/2. As I've figured the x and y acceleration to be equal this will give me a =1.74 m/s2.

So where have I gone wrong? What would be the correct procedure for solving this problem? I'm very new to physics so any help would be appreciated :)
 
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Anybody out there able to help at all?
 
It does not matter what angle you are considering as the magnitude of acceleration will be same (if no other force such as gravity are being considered). Hence just use Pythagoras theorem.

And do not be impatient. Members here are able to solve question much more difficult than this. Do not question the ability, in future.
 

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