Relative Velocity after collision

[merced]

"Two balls of the same mass approach each other with a relative velocity of 10 m/s, what is their relative velocity after the collision, which is presumed elastic?"

I assumed that the balls have equal and opposite velocities of 10 m/s.
Should the individual velocities be 5 m/s and -5 m/s (because 10 m/s is the relative velocity)?

When I solved the problem, the balls simply exchanged their velocities.

I said that their relative velocities after the collision are 10 m/s. However, this is wrong because there is only one relative velocity.
I think I have the concept wrong. Please clarify.

 

[Dorothy Weglend]

Solve the equations of conservation of momentum and conservation of energy (since this collision is elastic) for the relative velocities before and after the collision, and you will see the relationship.

Dorothy

 

[kyle8921]

Your understanding of the concept is correct. In this scenario, the relative velocity after the collision would still be 10 m/s because the balls simply exchanged their velocities. However, it is important to note that the individual velocities of the balls would have changed. One ball would now have a velocity of -5 m/s and the other would have a velocity of 5 m/s. The relative velocity refers to the velocity of one object relative to the other, and in this case, it remains the same.