$8\mathrm{.}49-.$ Moderators. Canadian nuclear reactors use heavy water moderators in which elastic collisions occur between the neutrons and deuterons of mass $2\mathrm{.}0$u $($see Example $8\mathrm{.}11$ in Section $8\mathrm{.}4).($a$)$ What is the speed of a neutron, expressed as a fraction of its original speed, after a head$-$on$,$ elastic collision with a deuteron that is initially at rest? $($b$)$ What is its kinetic energy, expressed as a fraction of its original kinetic energy? $($c$)$ How many such successive collisions will reduce the speed of a neutron to $1//59,000$ of its original value?