Physics

To solve this problem, we need to consider the motion of the two balls and apply the principles of energy conservation and kinematics. Here’s how we approach it step-by-step:

Analyze the motion of ball A before the collision

 

Ball A starts from rest at a height and slides down the ramp to reach the horizontal surface. The ramp is smooth, so there is no friction, and the ball will convert its potential energy into kinetic energy as it descends.

 

The initial potential energy of ball A is:

 

Since the ball starts from rest, its initial kinetic energy is zero:

 

At the bottom of the ramp, all of the potential energy has been converted into kinetic energy. The total kinetic energy of ball A at the bottom of the ramp is:

 

The kinetic energy of a moving object is related to its velocity by:

 

So, the velocity of ball A at the bottom of the ramp is:

 

Analyze the collision between ball A and ball B

Since the collision is elastic, both momentum and kinetic energy are conserved. The initial velocity of ball A before the collision is , and ball B is initially at rest. The two balls have the same mass, so after the elastic collision, ball A comes to rest, and ball B moves with the velocity equal to the initial velocity of ball A. Therefore: