A neutron of mass \(m\) and velocity \(v_{0}\) collides head-on with a \({ }^{235} U\) nucleus of mass \(M\) at rest in a nuclear reactor, and the neutron is absorbed to form a \({ }^{236} U\) nucleus.

(a) Find the velocity \(v_{A}\) of the \({ }^{236} U\) nucleus in terms of \(m, M\), and \(v_{0}\).

(b) The \({ }^{236} U\) nucleus subsequently fissions into two nuclei of equal mass, each emerging at angle \(\theta\) to the forward direction. Find the speed \(v_{B}\) of each final nucleus in terms of given parameters. Use classical Newtonian physics to solve the problem.