$(20$ points$)$ To create a very massive particle with mass M one can accelerate two

lighter particles $($such as protons$)$ with mass m for an inelastic collision between

them. In $$fixed$-$target$$ experiments one light particle is at rest and the other light

particle is accelerated to have a kinetic energy of Kfixed. In $$collider$$ experiments

both light particles are accelerated each to have a kinetic energy of Kcol and collided

head$-$on $($so that total momentum is zero$).$ Calculate the minimum kinetic energy

needed in both cases.

Which experiment would you prefer to fund if you want to create very massive

particles?