three c pls

3. A proton With kinetic energy T collides with a proton at rest. After the collision, the two protons travel at an angle 6/2 relative to the original proton direction. a) Show that c2302 = T2 + 2T'mc2 where p is the momentum of the incoming proton and m is the proton mass. [4 marks] b) Write down the relevant equations corresponding to the conservation of energy and momentum. [6 marks] c) Show that cos 6 T _ T + time2 You may use the identity cos2 a: = 5(1 + cos 2:3). [10 marks] d) If 9 = 60, determine the kinetic energies of the outgoing protons. [5 marks]