9. (Problem Solving)

Collision Problems

Start with momentum conservation: ${\vec{p}}_{i} = {\vec{p}}_{f}$ . If there are two objects, then $m_{1} v_{1 i} + m_{2} v_{2 i} = m_{1} v_{1 f} + m_{2} v_{2 f}$
Fill in what is given, and solve for what's left.
Notice that the masses $m_{1}$ and $m_{2}$ appear on both sides of the equation.
Remember that the velocities have direction and therefore sign: + or -.
If the two objects "stick together" after the collision, then they have the same velocity: $v_{1 f} = v_{2 f}$
If the problem involves something that comes apart (like a bomb), then their initial velocities are the same: $v_{1 i} = v_{2 i}$