Final answer:
In an elastic collision between two objects of equal mass, the principle of conservation of momentum and the conservation of kinetic energy are used to determine the final velocities of the objects post-collision. Given the provided velocities and direction of movement before the collision, the final velocity of object B can be calculated.
Step-by-step explanation:
When two objects of equal mass collide elastically, such as in the provided scenario where object A and object B collide, we can use the conservation of momentum and the conservation of kinetic energy to determine their velocities after the collision. According to the principle of conservation of momentum, the momentum before the collision must be equal to the momentum after. The formula for this principle is P1 + P2 = P'1 + P'2 where P is the momentum of each object before collision, and P' is the momentum afterward.
For the provided case, object A's initial momentum is the product of its mass and velocity (4.0 m/s), and object B's initial momentum is the product of its mass and velocity (8.0 m/s). After the collision, A is moving at 8.0 m/s in the -x-direction. Using the conservation of momentum, we can find out object B's velocity by equating the total initial momentum with the total final momentum since the masses are equal and the collision is elastic.
The kinetic energy is also conserved in elastic collisions, which means we can set up an equation equating the kinetic energy before and after the collision to find out the final velocity of object B. The formula for kinetic energy is KE = 1/2 m v2, where m is the mass and v is the velocity. Because the collision is elastic and the masses of object A and B are equal, we can conclude that object B must also have a change in kinetic energy consistent with an elastic collision, resulting in a specific final velocity.