We can use relativistic mechanics to calculate that it takes colliding beams of e-'s and e+'s each with energies of 45 GeV to produce a Z particle. But it takes a particle with an energy of 4050 GeV if it hits a fixed proton target, for which mc^2 = 1 GeV.
Question: If you have two beams with energy = 50 GeV for a colliding-beam collision, what energy is need for a fixed-target collision with a proton target (mc^2 = 1 GeV) to get the same available energy?