2. (15 points) Oscar has built a machine that pitches balls for his dog's enjoyment. As shown in the figure, a ball of mass m comes up through a tube and is deflected horizontally by a curved (circular) piece of metal of radius R. When the ball leaves the device at a height h above the ground, it has a launch speed v0. It travels through the air and lands a distance D from where it was launched. (You may neglect friction and air drag). (a) (5 points) If the ball lands a distance D from where it was launched, find an expression for the initial launch speed v0 when the ball emerges horizontally from the machine. Express your answer in terms of D or any of the other constants given in the problem and any relevant physical constants. (b) (5 points) Find an expression for the magnitude of the normal force FN exerted by the curved part of the machine on the ball just before the ball is launched horizontally from the tube. Express your answer in terms of h,D,m,R, and any relevant physical constants. (Note: If you could not find an expression for the speed v0 in part (a), you may express your answer here in terms of v0 ). (c) (5 points) Find an expression for the minimum launch speed vmin such that the ball will emerge horizontally from the pitching machine. Express your answer in terms of m,R, and any relevant physical constants. (Hint: If the ball doesn't emerge horizontally, it won't be in contact with the machine at the top of the curved metal arc)