Final answer:
Momentum for a system can be conserved in one direction while not being conserved in another if the directions are at a 90 degrees angle to each other, as seen when horizontal momentum is conserved but vertical momentum is not due to gravity. Therefore, the correct answer is option a) 90 degrees
Step-by-step explanation:
Momentum for a system can be conserved in one direction while not being conserved in another. The angle between these directions is 90 degrees.
An example of this is a situation where an object is moving in a frictionless environment horizontally, conserving momentum in the horizontal direction, but affected by gravity in the vertical direction, causing a change in momentum in that direction.
The conditions for momentum conservation are such that if there is zero net external force acting on a system in one direction (x-axis), then momentum is conserved in that direction. However, if there is a non-zero net external force acting on the system in a perpendicular direction (y-axis), momentum is not conserved in that perpendicular direction.
The angle between the directions can be 90 degrees. When momentum is conserved in one direction and not conserved in another, it means that there is no external force acting in the conserved direction, but there is an external force acting in the non-conserved direction.
This can be illustrated with the example of a spacecraft in orbit around a planet. The momentum of the spacecraft is conserved in the radial direction towards the planet, but not conserved in the tangential direction perpendicular to the radial direction. Therefore, the angle between the directions would be 90 degrees.
Therefore, the correct answer is option a) 90 degrees