Final answer:
Momentum can be conserved in one direction and not in another due to the presence of external forces that act only in certain directions. An example is pool balls colliding on a tilted pool table where horizontal momentum is conserved, but vertical is not. Understanding momentum conservation is critical in various contexts from simple collisions to understanding air resistance against a car.
Step-by-step explanation:
Momentum can indeed be conserved in one direction while not being conserved in another. This situation typically occurs when there are external forces acting on the system that affect motion in one direction but not in another. For momentum to be conserved in a particular direction, there must be no external net force acting along that axis. If external forces are present, momentum conservation can be complicated.
An example of this would be a pool table that is not level, causing gravity to have a component along the surface. When two pool balls collide on such a table, the momentum along the horizontal plane (ignoring the slight tilt) could be conserved, but the vertical component (which includes gravity) would not be conserved due to the external gravitational force. The angle between these two directions is 90 degrees since one is horizontal and the other is vertical.
Professional Application: In the context of a car's air resistance, this can be explained in terms of momentum and Newton's laws. As the car moves, it pushes air in its direction of motion, exerting a force on the air. In turn, the air exerts an equal and opposite force on the car (per Newton's third law), which we experience as air resistance. This is due to the car altering the momentum of the air in its direction of motion.
Regarding collisions, option b. Momentum is conserved, and kinetic energy is not conserved is often true for inelastic collisions, where objects stick together and kinetic energy is transformed into other forms of energy. In contrast, elastic collisions preserve both momentum and kinetic energy (option a). Collision examples such as a comet striking Earth or gas molecules demonstrate that conservation of momentum is only violated when a net external force acts on the system.