How to Solve Momentum & KE Equation 9.21

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SUMMARY

The discussion focuses on the derivation of Momentum and Kinetic Energy Equation 9.21, specifically addressing the calculations involved in solving for final velocities (v1f and v2f). The user expresses confusion regarding the substitution of two unknowns and the manipulation of equations 9.20 and 9.16. The key takeaway is that multiplying equation 9.20 by mass m1 and adding it to equation 9.16 simplifies the problem by eliminating the v1f term, enabling the calculation of v2f directly.

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  • Understanding of basic physics concepts such as momentum and kinetic energy.
  • Familiarity with algebraic manipulation of equations.
  • Knowledge of the specific equations involved: Momentum Equation (Pi=Pf) and Kinetic Energy Equation (Ki=Kf).
  • Ability to solve for unknown variables in equations.
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Students studying physics, particularly those tackling problems in mechanics and conservation laws, as well as educators looking for clear explanations of momentum and kinetic energy concepts.

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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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