A ball with a mass of #4 kg # and velocity of #3 m/s# collides with a second ball with a mass of #2 kg# and velocity of #- 4 m/s#. If #20%# of the kinetic energy is lost, what are the final velocities of the balls?

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Answer 1 · 2016-07-06T11:44:26

#{w_1 = -0.287855, w_2 = 2.57571}# or
#{w_1 = 1.62119, w_2 = -1.24238}#

Momentum conservation

#m_1 v_1+m_2v_2 = m_1 w_1 + m_2 w_2#

Kinetic Energy loss

#1/2m_1 w_1^2+1/2m_2 w_2^2 = gamma(1/2m_1 v_1^2+1/2m_2 v_2^2) #

Solving for #w_1,w_2# gives two solutions

#{w_1 = -0.287855, w_2 = 2.57571}# or
#{w_1 = 1.62119, w_2 = -1.24238}#