A vertically oriented uniform rod of mass M and lenght 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. Assume 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.
Ans: a) v=M/m root ( 2/3 gl) sin alpha/2
b) change in momentum = M [ ((1/6 gl)^0.5) sin alpha/2 ]
c) x=2l/3
Please reply with explanation!