Yes, we definitely use it for making the ball move faster. The squash racket has mass and speed, and as we know, the momentum is
So, when hitting the ball, the racket transfers its momentum to the ball. However, the racket has some flexible parts (strings and the racket's material itself), thus, the conservation of momentum is not the only one law we use in that situation. The law of conservation of energy is a very important part of the process, since the kinetic energy of the racket is wasted to heat and deformation of the ball and the racket, and after losing some amount of initial racket's kinetic energy, the ball acquires smaller kinetic energy.
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