Toly. What is your math background? You're using modeling techniques from an introductory algebra based physics class. These models are designed to introduce basic concepts of physics to someone with no math background.
Have you taken any physics courses that use modeling techniques from calculus? Have you taken any engineering courses? Are you self-taught?
The situation you are attempting to describe is complex and has many variables. If you relate these variables using simplified algebra, you won't be accurately modeling the situation.
We haven't even gotten into wind/air resistance. It would be a huge factor in this situation. I still have my notes from the first week of my ordinary differential equations class. If you want I can scan them and post them. They model a simplified view of wind resistance, in order to introduce the topic. There are many ways to model air resistance with increasing complexity and sophistication. Since I only studied math at the undergraduate level, I don't know them. I'm guessing you don't either.
Quit wasting people's time. This thread isn't for math oriented players at all. You're trying to use pre-algebra and algebra to model a dynamic, constantly changing situation. Hmmm, what discipline studies rates of change???? Calculus
The two objects you're examining aren't moving in space uneffected by other forces. The have constant mass, but they don't have constant velocity. They don't have constant acceleration!! Racket head acceleration is not constant!! It's not like two billiard balls with no outside forces at the time of the collision. The force exerted by the person on the racket is effecting the collision.
I can probably scan old notes from my differential equations courses if you want. Just go to google look up differential equations, and look up simplified models of motion. You're trying to use introductory techniques to describe a dynamic event? It won't work!