Using graphs to solve multi-dimensional momentum problems can be really helpful! Here’s how I do it:

1. Vector Diagrams: I start by drawing vector diagrams for each object. These diagrams show their momentum. We figure out momentum by using mass (which we call $m$) and velocity (which we show as $\vec{v}$). The momentum is calculated as $m \vec{v}$.

2. Breaking It Down: Next, I break these vectors into parts. Usually, we look at the x and y directions. If we're working in 3D, then we also add z. This makes the math simpler.

3. Total Momentum: Finally, I add up the parts separately. This helps me find the total momentum in each direction.

Using this visual method helps us understand how momentum works in different dimensions!