#"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)#

#"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#