Physics

To solve this problem, let’s analyze it step by step using the principles of elastic collisions and energy conservation.

 

Velocities before the collision:

Both balls are dropped from height h, so their velocity just before reaching the ground is calculated using energy conservation:

 

When ball B collides elastically with the ground, it reverses direction without losing speed because the ground is much more massive. After rebounding, ball B has a velocity:

(Negative sign indicates the upward direction.)

 

Collision between ball A and ball B:

Now, ball A and the rebounding ball B collide elastically. Before the collision:

Ball A's velocity: (downward, positive direction)

Ball B's velocity: (upward, negative direction)

 

For an elastic collision, we use the conservation of momentum and kinetic energy.

 

The conservation of momentum gives , where and are the velocities of ball A and ball B just after the collision.

 

Substituting , , and into the momentum - conservation equation:

.

 

For an elastic collision, kinetic - energy conservation .

Substituting , , and :

 

From , we have .

 

Substitute

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