Problem 1.275

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 $\alpha .$ Assuming that $m \ll M,$ 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.