Before we start accelerating the ball we should accelerate our arm and racquet with mass around 20 pounds. As result we create very big forward momentum 20pounds*50mph. If we stand on the ground we can transfer this momentum (force) to the mass of the Earth. Thus, our body still is able to rotate forward without any problem.
Suppose we jumped before contact. Then, according to one of the fundamental laws of physics – Conservation of Momentum, if one part of the body is given a forward momentum (arm), then some other part of the body (torso) simultaneously be given exactly the same momentum in the opposite direction (backward). But usually our arm is connected to torso, thus our arm also get some significant momentum directed backward. Thus, we inevitably will lose racquet/ball’s speed.
The jump into air before impact cannot increase serve power, quite the contrary!!!
Toly, this discussion has come up before and maybe I should just let it go, but I am concerned that since you are applying physics to support your arguments that someone might be convinced that you are correct. Respectfully, I don't believe you are correctly analyzing the physics involved in hitting a serve and, as I've mentioned before, your analysis would require that just about every high level player hits their serve in a sub-optimal way.
The key to this whole analysis is that the goal of getting the maximum velocity on the ball during a serve is to get the maximum velocity of the head of the racquet at impact. The velocity of the center of mass of the racquet, the arm, or any part of the body doesn't matter. It's just the velocity of the head of the racquet that matters. You also have to take into account how the human body is built and how our joints work.
Here's a link to Federer hitting a serve in super slow motion:
http://www.youtube.com/watch?v=InYd8IrFnkU
At about 0:26 he's in the trophy pose and starts to push with his legs. The vector of his leg push is almost totally up. It has a small component into the court, but it's almost all up. Note the path that the right arm and the racquet takes while this is happening. His upper arm is not going forward, it's going up also, about in line with the leg push. In fact his upper arm moves about 180° around his shoulder. At 0:26 his elbow was pointing down and the racquet was pointing up. At 0:31 the elbow is pointing up the racquet is pointing down. His upper arm is rotated back about as far as it can go without injury and his wrist is also supinated back about as far as it can go.
All the force from his legs pushing up has gone into getting his arm and wrist into this position. His legs are driving his whole body up towards the ball. The racquet has not started to come forward towards the ball.
The other place where he's using the reaction force from the ground is to start his core rotating. But note that his shoulders aren't level with the ground. His core is rotating about an axis that's about at 45° to the ground. His left shoulder was high and his right shoulder low at 0:26. Before his feet leave the ground at 0:31 his shoulders have started to trade places. By 0:32 his right shoulder will be high and his left shoulder low. His feet's contact with the ground help react the force generated by rotating his shoulders.
Also note how his left arm aids in the process of bringing his shoulders around more powerfully. The arm starts coming down at 0:26 also. The left arm coming down will tend to un-weight his feet. The leg push and the left arm motions are complimentary. The shoulder rotation is complete after his feet are completely off the ground, but the contribution of his left arm helps the motion.
At about 0:31, his feet have left the ground, so he's not going to get anymore benefit from pushing on mother earth. He has used all of his leg force to drive his body up, get his right elbow high, his wrist supinated (so consequently his racquet is cocked down), and to start his shoulder turn. His left arm has assisted in this process but has done about all that it can do.
The racquet face has still not begun to come forward towards the ball. The whole racquet will travel up towards the ball until 0:32. However because of the way a human arm works he has stored an incredible amount of energy. Everything that he's done up to this point was about storing energy. He has loaded the spring. He is now in the position to unleash that energy onto the ball.
From 0:32 to 0:34 the racquet comes forward into the ball. His arm whips up and into the ball with the racquet still lagging behind. Only when his arm is mostly extended does the whip get cracked and the racquet come around into the ball. Of course as the racquet comes forward something has to react this force. His feet have long since left the ground so he's not getting any help there. What reacts the racquet's forward velocity is the lean into the court that Federer had when he started his upward motion (the small component of leg push into the court), and the motion of his legs. Remember, the only thing that matters is how fast the head of the racquet is going. Every other part of his racquet and body can be going backwards (in theory anyway). In this video he's really bringing his knees up. Usually it's a bit more of a scissoring action between the right and left leg. Here's another video that shows that:
http://www.youtube.com/watch?v=vcjZ5r_YHV0
He's 180 lb human reacting a 12 oz racquet. He doesn't need that much force to react the racquet. This is the area that you've been focusing on, but you're missing the forest for the trees. What he has done by driving up towards the ball instead of staying in contact with the ground and moving forward is help load energy into the rest of his body and unleash that energy as quickly and as violently as possible onto the ball. In that last instant when the racquet finally does come toward the ball he can react the motion with other parts of his body. If he were to keep his feet on the ground as you prescribe then it would not be possible for him to as completely load up all of this energy into his joints. He could better react the force of the racquet going forward, but he would do so at the expense of completely loading all of the energy that he was able to load by pushing up rather than forward.
Sorry for the book, but I hope this makes sense.
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