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> Consider two objects $B\_1$ and $B\_2$ of equal mass $m$. The object $B\_2$ is stationary, while $B\_1$ is moving towards $B\_2$ with velocity $\mathbf{v}$. Suppose that after the collision, $B\_1$ and $B\_2$ have velocities $\mathbf{w}\_1$ and $\mathbf{w}\_2$ that are collinear with $\mathbf{v}$ and, moreover, point in the same direction as $\mathbf{v}$. Show that $|\mathbf{w}\_1|\leq|\mathbf{v}|/2$. (This is a very simple physics problem, not a mathematics problem!)
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Here is what I got: By conservation of momentum, we have:
$$ mv = mw\_1 + mw\_2 \\
v = w\_1 + w\_2 $$

Since they are collinear and in the same direction, we have $v\ge 0$, $w\_1\ge 0$, and $w\_2\ge 0$. Now, I am confused how I am supposed to prove that. 

It is my understanding that, for every possible value of $w\_2$, I'll have a different collision. And so, if we consider the special case where $v=6$ and $w\_2 = 1$, then by momentum conservation $w\_1 = 5$, we don't have $w\_1\le v/2$.

Am I doing something wrong? How do I prove what my book wants?