1) Energy ( i.e. really Large scale KE + PE) was conserved in the pendulum type motion that followed the collision. Delta PE = - delta KE and in this instance PE final = KE right after the collision
2) Momentum was conserved in the inelastic collision (even while some KE was converted to microscopic energy such as distortions in the rubber of the catcher and noise. IT IS NOT the fact that the mass of the catcher and ball is different from the mass of the ball alone that means KE is not preserved. It is the fact that they stuck together and there were losses of KE into hard to measure forms of energy and transfers of energy outside the system ( sound is an example of both) that kept KE from being conserved.
Energy conservation after the collision and momentum conservation during the collision were demonstrated to be true. This is true because the initial velocity ( launch speed) of the ball determined by a two stage calculation relying first on E conservation to find the v' after the collision and then using that v' and conservation of p to find the v of the ball before the collision i.e. its launch speed was confirmed by the previously proven projectile motion methods relating vx to delta x.
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