Step 1:

Mass of the ball A is .

Let the initial speed of ball A before collision is .

Ball A of mass m makes a head-on elastic collision with a second ball B, which is at rest.

Thus, speed of ball B before collision is .

Let the mass of the ball B as .

Ball A rebounds with a speed equal to 0.45 of  its original speed after collision.

Therefore, the final speed of ball A after collision is .

Let the final speed of ball B after collision is .

Conservation of momentum for elastic collisions: .

Substitute corresponding values in the formula.

Step 2:

The relative velocity of one particle with respect to the other is reversed by the collision.

.

Substitute corresponding values in the formula.

Substitute in expression (1).

Thus, mass of the ball B is .

Solution:

Mass of the ball B is .