Very informative and liked how you went through different problems. Just want to clarify one thing at the end of problem 6. The ball is going in a direction normal to the bat, meaning it travels horizontal in the positive X direction until it is hit by the bat. Its reaction is that the the ball goes straight up 90 degrees (Positive Z direction). Looking at your coordinates, all of this motion of the ball is happening in the X-Z plane. The sum of the forces triangle is in the same X-Z plane. Correct? It was a bit puzzling at first to figure out that the ball was going up at 90 degrees but the momentum was at an angle theta of 63.4 degrees. This must mean that the ball did not hit on the centerline of the bat, but biased towards the upper side.