What Force is Needed for 1.5 m/s² Acceleration in the +y Direction?

[DaOneEnOnly]

Homework Statement

Two forces act on an object of mass 2.5kg; force F1 that is directed alont the +x-direction and has magnitude of .50N and force F2 that points at a 45 degree angle in the +y and -x quadrant and has magnitude 2.0N. Find the additional force, if any such that the object will accelerate in the +y direction with magnitude 1.5m/s/s.

Homework Equations

F=ma
Fnet=F1+F2+F3+etc...
F=Fsin$$\theta$$

The Attempt at a Solution

F_nety= F₂sin$$\theta$$+F_X-F_g

F_X= missing force= ?
F_nety= (2.5kg)(1.5m/s/s)= 3.75N
F₂sin$$\theta$$= 1.414N
F_g= 2.5*9.8=24.5N

3.75 = F_X + 1.414 -24.5
F_X= 26.84N

I'm not sure if I'm even trying to go about the problem correctly.

The selected answers in the back of the book has the answer as:
(0.91N)i+(2.3N)j

so I'm really confused.

 

[rl.bhat]

Let the third force be xi + yj.
Take x and y components of all the three forces. Since the resultant force is along y axis, total x-component must be zero.
Hence total y component must be equal to ...?