According to the saving of the momentum law, the total momentum before collision equals to the total momentum after collision
After collection, the 2 carts lock together, one body with a mass [tex]m=m_{1}+m_{2}[/tex] and velocity [tex]v[/tex]
[tex](P_{1}+P_{2})_{before}=P_{after}[/tex]
from the definition of the momentum [tex]P=mv[/tex]
[tex]P_{1,before}=m_{1}v_{1,before}=0.180*0.80=0.144kg.m/s[/tex]
[tex]P_{2,before}=m_{2}v_{1,after}=0.100*0=0kg.m/s[/tex]
thus
[tex]P_{after}=(0.144+0)_{before}=0.144 kg.m/s[/tex]
we calculate the velocity
[tex]v=\frac{P}{m}=\frac{0.144}{0.180+0.100}= 0.514m/s[/tex]
