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

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To achieve an acceleration of 1.5 m/s² in the +y direction for a 2.5 kg object, the net force required is 3.75 N. Two forces are already acting on the object: F1 at 0.50 N in the +x direction and F2 at 2.0 N at a 45-degree angle, contributing approximately 1.414 N to the +y direction. The gravitational force acting on the object is 24.5 N downward. To balance the forces and achieve the desired acceleration, an additional force in the +y direction must be calculated, resulting in a required force of approximately 26.84 N in the +x direction. The confusion arises from the need to ensure that the net force in the x-direction equals zero while achieving the necessary y-component.
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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


Fnety= F2sin\theta+FX-Fg

FX= missing force= ?
Fnety= (2.5kg)(1.5m/s/s)= 3.75N
F2sin\theta= 1.414N
Fg= 2.5*9.8=24.5N

3.75 = FX + 1.414 -24.5
FX= 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.
 
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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 ...?
 
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