# Tag Info

This problem has a recursive flavor that we'll not try to avoid. Conservation of momentum tells us that $$m v_0 + (p+n-1)m v(n-1) = (p+n)m v(n).$$ Imposing the boundary condition $v(0)=0$ we find $$v(n) = \frac{n}{n+p}v_0$$ as claimed. Let $a_n$ be the time at which the $n$th bullet strike occurs. We have $a_1=x_0/v_0$ and v_0 (a_n - T) = v_0 ...