To understand the vector nature of momentum in the case in which two objects collide and stick together. In this problem we will consider a collision of two moving objects such that after the collision, the objects stick together and travel off as a single unit. The collision is therefore completely inelastic. You have probably learned that "momentum is conserved" in an inelastic collision. But how does this fact help you to solve collision problems?

The vector nature of momentum in the case in which two objects collide and stick together helps us to understand conservation of linear momentum because of the direction of the two objects. This can occur in three different cases.

1. If both are moving in the same direction, then,

[tex]M_{1}V_{1} + M_{2} V_{2}[/tex] = [tex](M_{1}+M_{2} )V[/tex]

2. If they are moving in opposite direction

[tex]M_{1}V_{1} - M_{2} V_{2}[/tex] = [tex](M_{1}+M_{2} )V[/tex]

3. If one object is at rest,

[tex]M_{1}V_{1} + 0[/tex] = [tex](M_{1}+M_{2} )V[/tex]

In this problem we will consider a collision of two moving objects such that after the collision, the objects stick together and travel off as a single unit. The collision is therefore completely inelastic.

Therefore, with the use of the formula by taking the direction of the object into cognizance does help to solve collision problems.

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