inelastic collision problem

[mbashir3628]

6) Assuming disks A and B collide inelastically as in the diagram below, what will the final momentum of the combined two disks be after the collision?

A: (in the x-direction) has m = 5kg and v = 10 m/s
B: (in the y-direction) has m = 20kg and v = 3.75m/s

I know that Total Final momentum = Total initial momentum, but why do you use the following equations to solve the problem:

Pi2 = Px2 + Py2
Pi = √(Px2 + Py2) --> isn't that the eq. for the magnitude of the initial velocity for projectile motion?

where
Px = mv = 5 kg x 10 m/s = 50 kg m/s
Py = mv = 20 kg x 3.75 m/s = 75 kg m/s

Pi = √(Px2 + Py2)
Pi = √[(50 kg m/s)2 +( 75 kg m/s)2]
Pi = √[2500 + 5625]
Pi = √(8125)
Pi ≈ 90 kg m/s

---Why don't you do the following (since it's an inelastic collition)??:

MA∙VAi + MB∙VBi = (MA+MB)∙Vf
(5kg)(10m/s) + (20kg)(3.75m/s) = (5kg + 20kg)∙Vf

and when this is done, you get Vf (which is A and B combined) to be 5m/s. . .making the momentum after the collision of the combined A and B to be 125 kg∙m/s