HSC Physics Harder Mechanics Questions

A sheet of harder mechanics questions appears below.

  1. An elastic collision occurs between an alpha partice of mass m and a stationary nucleus of mass M. After collision the alpha particle moves at an angle 𝜃 to its initial direction and the nucleus moves at an angle ϕ to the initial direction of the alpha particle. Show that m/M = sin(2ϕ + 𝜃)/sin𝜃 .