Consider a one- dimensional elastic collision between a moving object A and an object B initially at rest. How would you choose the mass of B, in comparison to the mass of A, in order that B should recoil with (a) the greatest speed, (b) the greatest momentum, and (c) the greatest kinetic energy?

When a massive body collides with a light body at rest, the velocity of the massive body remains practically unchanged while the light body starts moving with a velocity which is nearly double the velocity of massive body. Therefore the object B should recoil with greatest speed if it is light comparison to the mass A.
Momentum of the body is equal to the mass of the body time’s velocity of the body. Since the object B should recoil with greatest speed if it is light comparison to the mass A, therefore the object B should recoil with greatest momentum if it is light comparison to the mass A.
Kinetic energy of the body (K) is defined as the,
K = ½ mv² …… (1)
Where m is the mass of the body and v is the velocity of the body.
From equation (1), kinetic energy of the body is proportional to the square of the velocity of the body. Since the object B should recoil with greatest speed if it is light comparison to the mass A, therefore the object B should recoil with greatest kinetic energy if it is light comparison to the mass A.