A 10 Kg body is moving at vi=i+j m/s and after its explosion it breaks into 3 pieces. The first piece is 3 Kg and goes through to v1=12·i+2·j m/s, the second body weights 5 Kg and goes through to v2=2·i+12·j m/s. What velocity does the third piece reach?



  • Total mass of th body and velocity before the explosion: mi=10 kg;vi=i+j m/s
  • Mass and velocity of the first piece: m1=3 kg;v1=0.5·i+2·j m/s
  • Mass and velocity of the second piece: m2=5 kg;v2=2·i+0.5·j m/s


Firstly, we can know the mass of the third piece, since the body had 10 kg before the explosion, the mass of the third piece will be m3 = mT - m1 - m2 = 2 kg. Because the linear momentum conservation theorema, the quantity of motion before and after the explosion mus be preserved:

F=0 p= constantpi=pfmT·vi=m1·v1+m2·v2+m3·v3v3=mT·vi-m1·v1-m2·v2m3=10-1.5-10·i+10-6-2.5·j2=-0.75·i+0.75·j

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Related sections
F=0 p= constantdpdt=0