Two particles move perpendicular to each other until they collide. (See image) Particle 1 has mass m and momentum of magnitude 2p, and particle 2 has mass 2m and momentum of magnitude p. Note: Magnitudes are not drawn to scale in any of the figures.

Suppose that after the collision, the particles "trade" their momenta, as shown in the figure. That is, particle 1 now has magnitude of momentum p , and particle 2 has magnitude of momentum 2p; furthermore, each particle is now moving in the direction in which the other had been moving. How much kinetic energy, K_lost , is lost in the collision?
Express your answer in terms of m and p.

Consider an alternative situation: This time the particles collide completely inelastically. How much kinetic energy K_lost is lost in this case?
Express your answer in terms of m and p.