Understanding the Law of Inertia with a Physics Scenario

Why does the student not move backward in this situation?

When the student throws the brick with some force, the brick moves forward with that force. Since Newton's third law says every action has an equal and opposite reaction, the brick also exerts an equal and opposite force on the student that would cause them to move backward. However, the student is standing on frictionless ice, which means that they cannot experience any frictional force that would cause them to move backward. Hence, the student remains stationary and does not move backward.

Resulting Velocity of the Student

Since the student is at rest and there is no frictional force acting on them, they will continue to be at rest as per the first law of Newton or the law of inertia. The force of the student is equal to the force on the brick, but in opposite direction since the student and the brick are exerting the same amount of force on each other, but in opposite directions. The momentum of the system before and after the throw must be equal. The momentum of the student, the brick, and the whole system remains zero as they were both at rest. Thus the velocity of the student is zero or remains at rest before and after the throw of the brick. Therefore, the resulting velocity of the student is zero.