## Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson

# Chapter 9 - Exercises and Problems - Page 165: 57

#### Answer

$\frac{2}{5}v, \frac{7}{5}v$

#### Work Step by Step

We know the following equation for elastic collisions: $v_{1f}=\frac{m_1-m_2}{m_1+m_2}v_{1i}+\frac{2m_2}{m_1+m_2}v_{2i}$ Thus, we find: $v_{1f}=\frac{4m-m}{5m}v+\frac{2m}{5m}(2v)=\frac{7}{5}v$ We use conservation of momentum to obtain: $2mv+4mv = \frac{7}{5}(4m)v+mv_f$ $v_f = \frac{2}{5}v$

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