Here is a case where bullets are fired into blocks, and by measuring what happens afterwards allows us to figure out the speed of the bullet before the collision. A classic example is a ballistic pendulum, and this is compared to a similar spring problem. Because the collisions are INelastic, kinetic energy before and after is not the same (KEo > KEf). But, conservation of momentum is what connects the before and after pictures of such collisions. Check it out.