How to Solve Momentum & KE Equation 9.21

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Equation 9.21 is derived from the conservation of momentum and kinetic energy principles, specifically using the equations Pi=Pf and Ki=Kf. The user struggles with substituting two unknowns and suggests multiplying equation 9.20 by m1 and adding it to equation 9.16 to eliminate the v1f term. This method allows for solving for v2f, and a similar approach can be applied to find v1f. Clarification on the calculation steps is needed to identify where the mistakes occurred. Understanding these substitutions is crucial for correctly deriving the equation.
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Homework Statement



Can someone show me how equation 9.21 was derived?? I messed up on my calculations

Homework Equations



Pi=Pf
Ki=Kf

The Attempt at a Solution



I don't know where i went wrong in terms of substituting 2 unknowns
 

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Multiply 9.20 by m1 and add 9.16. The v1f term disappears allowing you to solve for v2f. Similarly for solving for v1f.
 

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