Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the problem and the magnitude of the eight ball's initial velocity, v.

Complete Question

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The expression for the velocity of the sixth ball is

Explanation:

From the question we are told that

     The mass of the 8 ball is  

      The initial velocity of the 8 ball is  

      The initial velocity of the 6 ball is  

         The mass of the 6 ball is  

Generally from the law of momentum conservation is  

Now along the y  axis

So

=>  

Now along the x  axis

So

=>    

substituting for in the above equation

=>      

=>

 given that  

=>

=>

=>

=>

converting back  to  

So

multiply through by  

=>  

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