A proton of mass m_p with initial velocity v_0 collides with a lithium-7 nucleus, mass 7m_p, that is initially at rest. The proton leaves the point of impact at angle 50° with its original line of motion. Find the final velocities of each particle if:

a) the collision is perfectly elastic.

b) the collision is inelastic and that Q is equal to one-third of the initial kinetic energy of the proton.