In an elastic collision, both momentum and kinetic energy are conserved. In this case, we have two objects of mass $m$, moving toward each other with velocities $v$ and $2v$, respectively.

Key Points for an Elastic Collision:

• The objects will bounce off each other, so their directions of motion will reverse after the collision.
• The total momentum and kinetic energy of the system are conserved.
• For a one-dimensional elastic collision between two objects of equal mass, the velocities of the objects are exchanged. That is, after the collision, the object that was moving at velocity $v$ will move at velocity $2v$, and the object moving at velocity $2v$ will move at velocity $v$.

Analysis of the given options:

Option 1:

• Green object (left): velocity $v$ → this object moves toward the right with a velocity of $2v$ after the collision.
• Blue object (right): velocity $2v$ → this object moves toward the left with a velocity of $v$ after the collision.

This correctly represents the velocity exchange that occurs in an elastic collision.

Option 2:

• Both objects are shown moving to the right with velocities $2v$.
• This does not represent a typical outcome of an elastic collision where the velocities should change directions.

Option 3:

• Green object (left): velocity $2v$ → after the collision, it moves with a velocity $v$, but in the opposite direction.
• Blue object (right): velocity $v$ → after the collision, it moves with velocity $2v$, in the opposite direction.

This option also seems to represent the direction and velocities correctly.

Conclusion:

Option 1 correctly shows the direction and velocities after an elastic collision. It follows the rules of momentum and energy conservation for a one-dimensional elastic collision, where the objects exchange their velocities.

Would you like more details on the physics of elastic collisions, or any clarification on the other options?

Related Questions:

1. How do elastic collisions differ from inelastic collisions in terms of momentum and energy?
2. What is the equation for momentum conservation in a two-body elastic collision?
3. How would the result change if the masses of the objects were not equal?
4. How can the velocity of the objects be calculated in an elastic collision using momentum equations?
5. What is the significance of kinetic energy conservation in elastic collisions?

Tip: For collisions involving equal masses, it's useful to remember that they often simply exchange velocities, making the calculations easier.