STICKY OBJECTS
 

Look at Fig. 1. The two objects have masses m₁ and m₂, and they are moving at speeds v₁ and v₂, respectively. The velocity vectors v₁ and v₂ are not specifically shown here, but they point in the directions shown by the arrows. At A in this illustration, the two objects are on a collision course. The momentum of the object with mass m₁ is equal to p₁ = m₁v₁; the momentum of the object with mass m₂ is equal to p₂ = m₂v₂.
At B, the objects have just hit each other and stuck together. After the collision, the composite object cruises along at a new velocity v that is different from either of the initial velocities. The new momentum, call it p, is equal to the sum of the original momentums. Therefore:
p = m₁v₁+ m₂v₂
The final velocity v can be determined by noting that the final mass is m₁+ m₂. Therefore:
p = (m₁+ m₂)v
v = p/(m₁+ m₂)

Fig. 1. (a) Two sticky objects, both with constant but different velocities, approach each other. (b) The objects after the collision.