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"let the velocities of objects after collision be "v_1' " and " v_2^'
P_1':" momentum of the red ball after collision"
v_1^':"velocity of the red ball after collision"
P_1^'=m_1*v_1^'
P_1^'=5*v_1^'
P_2^':"momentum of the blue ball after collision"
v_2^':"velocity of the blue ball after collision"
P_2^'=2*v_2^'
"vectorial sum of the momentums after collision :"
P_a=P_1^'+P_2^'
P_a=5v_1^'+2v_2^'
P_b=P_a" conservation of momentum"
10=5v_1^'+2v_2^'" "(1)
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"the total velocities of the objects must be equal"
v_1+v_1^'=v_2+v_2^'
2+v_1^'=0+v_2^'
color(red)(v_2^'=2+v_1^')" "(2)
"use (1)"
10=5v_1^'+2(color(red)(2+v_1^'))
10=5v_1^'+4+2v_1^'
10=7v_1^'+4
10-4=7v_1^'
6=7v_1^'
color(green)(v_1^'=6/7)" "m/s
"use (2)"
v_2^'=2+color(green)(6/7)
v_2^'=20/7" "m/s
