A ball with a mass of #5 kg # and velocity of #6 m/s# collides with a second ball with a mass of #3 kg# and velocity of #- 2 m/s#. If #40%# of the kinetic energy is lost, what are the final velocities of the balls?

1 Answer
May 18, 2016

#((v_1^a = 2.4, v_2^a = 4), (v_1^a = 3.6, v_2^a = 2))#

Explanation:

Calling #v_1^b, v_2^b# and #v_1^a,v_2^a# the velocities #b#-before and #a#-after collision we can equate:
#m_1 v_1^b + m_2 v_2^b = m_1 v_1^a + m_2 v_2^a#
and
#(1/2m_1 (v_1^b)^2 + 1/2 m_2 (v_2^b)^2) mu = (1/2m_1( v_1^a)^2 + 1/2 m_2 (v_2^a)^2)# with #mu = 0.4#
Solving for #v_1^a, and v_2^a# we obtain two possible arrangements
#((v_1^a = 2.4, v_2^a = 4), (v_1^a = 3.6, v_2^a = 2))#