As part of a carnival game, a 0.528-kg ball is thrown at a stack of 23.3 cm tall

Question

As part of a carnival game, a 0.528-kg ball is thrown at a stack of 23.3 cm tall, 0.403-kg objects and hits with a perfectly horizontal velocity of 12.3 m/s. Suppose the ball strikes the very top of the topmost object (the top bottle in a 3 bottle pyramid). Immediately after the collision, the ball has a horizontal velocity
of 3.35 m/s in the same direction, the topmost object now has an angular velocity of
4.83 rad/s and all the objects below are undisturbed. If the objects center of mass is located
16.3 cm below the point where the ball hits, what is the moment of inertia of the object in
kg x m^2 ?

part b) What is the center of mass velocity of the tall object immediately after it is struck?
(give answer in units of m/s)

Explanation / Answer

a) momentum conservation gives .528*12.3=.528*3.35+ I w^2*r -> I=1.24 kg/m^2 b)velocity/wrt gnd= 4.83*23.3/100=1.12m/s => Vel of Centre of mass= 1.12*1/3( since there are three bottles and only one in motion)=.375m/s

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