#"using the equation (1)"#
#5*12+9*0=5*u_1+9*u_2#
#60+0=5*u_1+9*u_2#
#60=5*u_1+9*u_2" (a)"#
#"using the equation (3)"#
#12+u_1=0+u_2#
#u_2=12+u_1 " (b)"#
#"now use (a)"#
#60=5*u_1+9*(12+u_1)#
#60=5*u_1+108+9*u_1#
#60-108=14*u_1#
#-48=14*u_1#
#u_1=-48/14=-24/7 m/s#
#"finally ;use (b)" #
#u_2=12-24/7#
#u_2=(84-24)/7#
#u_2=60/7" "m/s#
#"testing"#
#"The Total Kinetic Energy before collision:"#
#E_b=1/2*5*12^2+0#
#E_b=72*5=360J#
#"The Total Kinetic Energy after collision:"#
#E_a=1/2*5*(-24/7)^2+1/2*9*(60/7)^2#
#E_a=(5*576)/(2*49)+(9*3600)/(2*49)#
#E_a=(2880+32400)/98#
#E_a=35280/98#
#E_a=360J#
#color(green)(E_b=E_a)#