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 lt lt 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.

Answer

`[(M)/(m)sqrt((2gl)/(3))"sin"(alpha)/(2),Msqrt((gl)/(6))"sin"(alpha)/(2)]`