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.