Question

true or false: in a two - dimensional collision, momentum can only be conserved in one dimension, not both.truefalseobject 1 is moving in the positive x - direction. it collides with a second object that is initially at rest. the collision is not head - on, so the objects move off in different directions after the collision (see figure). what must be true about the total momentum of object 1 and object 2 in the y - direction after the collision?the total momentum in the y - direction after the collision will point in the positive y - direction, because object 2 has a greater mass.the total momentum in the y - direction after the collision will point in the negative y - direction, because object 1 has a greater speed after the collision.the total momentum in the y - direction after the collision will be equal to zero.

Explanation:

Step1: Recall the law of conservation of momentum

The law of conservation of momentum states that the total momentum of an isolated system remains constant. In a two - dimensional collision, if there is no external force acting on the system in the \(y\) - direction (which is a common assumption in such problems unless stated otherwise), the total initial momentum in the \(y\) - direction is \(p_{iy}=0\) (since object 1 is moving in the \(x\) - direction and object 2 is at rest initially).

Step2: Apply the law of conservation of momentum in the \(y\) - direction

According to the law of conservation of momentum \(p_{iy} = p_{fy}\). Since \(p_{iy}=0\), we have \(p_{fy}=0\).

Answer:

False, The total momentum in the \(y\) - direction after the collision will be equal to zero.