What makes a collision 2D?

In my mechanics course, we've covered 1D and 2D collisions. However, what physical factors determine whether a collision will be 1 or 2 dimensional?

To make the question more precise, consider a mass $$m_1$$ with velocity $$u_1$$ approaching a stationary mass $$m_2$$. After the collision, $$m_1$$ and $$m_2$$ have velocities $$v_1$$ and $$v_2$$, respectively. What properties must $$m_1$$, $$m_2$$ and $$u_1$$ have for $$u_1$$, $$v_1$$ and $$v_2$$ to be parallel?

• Jan 10, 2019 at 20:42

The problem is underspecified. Consider the collision in the centre of mass frame, where the particles have momentum $$\vec{p}$$ and $$-\vec{p}$$. Then so long as after the collision both particles come out in opposite directions with equal momenta both momentum and energy will be conserved. Thus you can't predict the final scattering angle from only the initial speeds and masses.