# Forces and acceleration

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

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 :)