$7[20$ pts$]$ A neutron collides elastically with a helium nucleus $($at rest initially$)$ whose mass is $4$ times that of the neutron. The speed of the neutron was $6\mathrm{.}0{10}^5\frac{m}{s}.$ After the collision the helium nucleus is observed to go off at ${}_{He}^{\text{'}}=45.$ Set up and simplify the equations necessary to find the final velocities of the neutron and the helium nucleus.

Do not solve