Two balls have the same mass. One ball moving along the positive x-axis and the other ball moving along the positive y-axis undergo perfectly inelastic collision. What can you say about the motion of the balls after the collision?

a) the balls stick and move together
b) the ball separate immediately
c) the first ball stops while the other ball start moving
d) the two balls travel off in opposite directions, 180 degree apart.

Inelastic collision means the two objects do not rebound and move at a common velocity.

Yes, choice a is correct.

a) the balls stick and move together

To determine the motion of the balls after the collision, we need to consider the conservation of momentum. The momentum of an object is given by the product of its mass and velocity.

Let's break down the scenario step by step:

1. We have two balls with the same mass. Let's call them ball A (moving along the positive x-axis) and ball B (moving along the positive y-axis).

2. The collision is described as perfectly inelastic. In a perfectly inelastic collision, the two objects stick together and move as one after the collision.

3. Since the balls stick together, their masses combine to form a single object. The resulting object has a new mass equal to the sum of the individual masses of ball A and ball B.

4. After the collision, the combined object's motion will depend on the initial velocities of the individual balls.

- If the initial velocity of ball A is zero and the initial velocity of ball B is zero, the combined object (after the collision) will have zero velocity, and all motion will stop. Therefore, option c) is incorrect.

- If the initial velocities of both balls A and B are non-zero, the resulting combined object will continue to move with a new velocity determined by the conservation of momentum.

5. The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, as long as no external forces are involved.

- The momentum of ball A along the x-axis before the collision is mass of A times velocity of A.
- The momentum of ball B along the y-axis before the collision is mass of B times velocity of B.

6. Since the masses of ball A and ball B are the same, the momenta before the collision are equal in magnitude, but they act in perpendicular directions.

7. In a perfectly inelastic collision, the resulting combined object moves in the direction of the total momentum vector.

- Since the momenta of ball A and ball B are equal in magnitude but act in perpendicular directions, the total momentum vector after the collision will also be equal in magnitude to the initial momenta, but at a 45-degree angle from both the x-axis and y-axis.

8. Hence, the correct answer is d) the two balls travel off in opposite directions, 180 degrees apart.

By applying the principles of conservation of momentum and understanding the characteristics of perfectly inelastic collisions, we can determine the correct option without any further calculations.