Answer
The x-component of the deuteron's velocity after the collision is $\frac{v_i}{2}$
The y-component of the deuteron's velocity after the collision is $-\frac{v_i}{6}$
Work Step by Step
Let $M$ be the mass of the neutron.
By conservation of momentum, the final momentum of the system is equal to the initial momentum.
We can find the horizontal component $v_x$ of the velocity of the deuteron:
$(2M)~v_x +(M)~(0) = M~v_i$
$v_x = \frac{v_i}{2}$
The x-component of the deuteron's velocity after the collision is $\frac{v_i}{2}$
We can find the vertical component $v_y$ of the velocity of the deuteron:
$(2M)~v_y +(M)~(\frac{v_i}{3}) = (M)~(0)$
$(2M)~v_y = 0 -(M)~(\frac{v_i}{3})$
$v_y = -\frac{v_i}{6}$
The y-component of the deuteron's velocity after the collision is $-\frac{v_i}{6}$
