Final answer:
In an elastic collision between two objects of equal mass, where one object's post-collision velocity is known, the other object's velocity can be determined using the conservation of momentum. For the given velocities before the collision, the missing velocity of the second object, mass B, after the collision is 4 m/s.
Step-by-step explanation:
The subject of this question is Physics, specifically related to the conservation of momentum and kinetic energy in collisions. We can find the missing velocity of mass B using the principle of conservation of momentum. Before the collision, both objects A and B have equal mass, so we can simply compare the velocity vectors.
Since momentum is conserved and the masses are equal, the initial momentum (mass times velocity) for A and B combined is zero because they are moving in opposite directions with the same magnitude of velocities (4.0 m/s and 8.0 m/s). After the collision, we know mass A has a velocity of 8.0 m/s in the -x-direction. Therefore, using the conservation of momentum, mass B must have a velocity of 4.0 m/s in the +x-direction, because the sum of the momenta after the collision must equal the initial momentum, which is zero.
(b) Confirming with kinetic energy, as it's conserved in an elastic collision, the kinetic energy before and after the collision should be the same. Before the collision, the kinetic energy can be calculated using 0.5mv² for each object. After the collision, the kinetic energy of object A must be equal to the combined kinetic energy before the collision. As object A has the higher velocity post-collision, the kinetic energy is higher, so object B must have a lower velocity to conserve kinetic energy. Thus, we can conclude that mass B must be moving with a velocity of less than its initial velocity, i.e., 4.0 m/s.
The correct option for the velocity of mass B after the collision is therefore (C) 4 m/s.