**P. 4310.** An air gun is modelled such that initially there is some compressed air in a container of volume *V*_{1}, at a pressure of *p*_{1}. In the barrel there is a small projectile of mass *m* right in front of the container's opening. *a*) How long should the barrel be in order to accelerate the projectile to the greatest speed? *b*) What can the maximum speed of the projectile be? (Neglect friction and the leaking of the high-pressure air.) *Data:* *m*=0.51 g, the inner diameter of the barrel is 4.5 mm, *p*_{1}=2 MPa, *V*_{1}=1 cm^{3}.

(5 points)