A vertically oriented uniform rod of mass M and length l can rotate about its upper end. A horizontally flying bullet of mass m strikes the lower end of the rod and gets stuck in it; as a result, the rod swings through an angle a. Assuming that m << M, find:
(a) The velocity of the flying bullet;
(b) The momentum increment in the system “bullet-rod” during the impact; what causes the change of that momentum;
(c) At what distance x from the upper end of the rod the bullet must strike for the momentum of the system “bullet-rod” to remain constant during the impact.