 After a 100% inelastic collision and a 100% elastic collision we have a third application of linear momentum which is explosions. I wrote it here on top of my inelastic collision notes because it actually is the same thing. If you think about it, in inelastic collisions you have two objects moving initially and then one object moving at the end. They stick together. Now in an explosion you have one big object that moves together and then is being ripped apart by the explosion and ends up being two objects or more than two objects moving in different directions. So what I had to flip is what we have before and what we have after. So now before we have one object traveling at the initial velocity and after the explosion we have the two parts in which the object fell apart moving in different directions. Kinetic energy as in an inelastic collision is not conserved. In the inelastic collision the energy went down so your final energy was lower. Why? Because there was a negative work done in order to deform the material during the collision. In this case in the explosion the energy released through the chemical reaction will definitely provide a positive work therefore your kinetic energy at the end is higher than it was before. Linear momentum however is conserved as an inelastic and elastic collision. For inelastic collision we had two parts moving initially becoming one part at the end. Now we have to flip this around. We had one object with a total mass traveling at some initial velocity which then rips apart and gives us two separate objects traveling at each their own velocity. A good application of this explosion equation here is the rocket equation. I have a special video about how to get the rocket equation based on this linear momentum conservation equation.