力学分析重车撞轻车

First, a disclaimer: I'm rusty at physics, even in its most elementary form. But I'll attempt to write down equations, solve them, and explain the results.

Let's assume that two vehicles, of mass m1 and m2, moving towards each other at velocities v1 and v2 (without loss of generality, v1>0, v2
The outcome of this collision is governed by two conservation laws:

1. Kinegic energy is conserved. Thus

0.5*m1*u1*u1 + 0.5*m2*u2*u2 = g * (0.5*m1*v1*v1 + 0.5*m2*v2*v2),

2. Momentum is conserved. Thus

m1*u1 + m2*u2 = m1*v1 + m2*v2.

This set of quadratic equations produce two sets of solutions, one of which under g=1 leads to u1=v1 and u2=v2 (in other words, no collision) and should be discarded. The valid solution can easily be obtained on say Mathematica, and I won't bother to list it here. For the ensuing discussion, it doesn't matter.