Understanding the Problem:
- Two balls are approaching each other with the same speed.
- The collision between the balls is elastic.
- After the collision, one of the balls comes to rest.
- We need to find the mass of the other ball.

Key Concepts:
- Elastic Collision: In an elastic collision, both momentum and kinetic energy are conserved.
- Momentum: Momentum is the product of an object's mass and its velocity. It is a vector quantity.
- Kinetic Energy: Kinetic energy is the energy possessed by an object due to its motion. It depends on mass and velocity and is a scalar quantity.

Solution:

Step 1: Understanding Elastic Collision
- In an elastic collision, both momentum and kinetic energy are conserved.
- Momentum is conserved in both the x and y directions.
- Kinetic energy is conserved in the x direction.

Step 2: Applying the Conservation of Momentum
- Let the mass of the first ball be m1 and the mass of the second ball be m2.
- Since both balls are approaching each other with the same speed, the velocity of the first ball is v1 and the velocity of the second ball is -v2 (opposite direction).
- Using the conservation of momentum in the x direction, we have:
m1 * v1 + m2 * (-v2) = 0
m1 * v1 = m2 * v2

Step 3: Applying the Conservation of Kinetic Energy
- After the collision, the first ball comes to rest, so its final velocity is 0.
- Using the conservation of kinetic energy in the x direction, we have:
(1/2) * m1 * v1^2 + (1/2) * m2 * v2^2 = 0
(1/2) * m1 * v1^2 = (1/2) * m2 * v2^2

Step 4: Solving the Equations
- From the equation obtained in step 2, we get:
v1 = (m2 * v2) / m1

- Substituting this value in the equation obtained in step 3, we have:
(1/2) * m1 * ((m2 * v2) / m1)^2 = (1/2) * m2 * v2^2
(m2^2 * v2^2) / m1 = v2^2
m2^2 = m1

- Taking the square root of both sides, we get:
m2 = sqrt(m1)

Step 5: Calculating the Mass of the Other Ball
- Since the mass of the ball that comes to rest is given as 3 kg, we can find the mass of the other ball using the equation obtained in step 4:
m2 = sqrt(3)
m2 ≈ 1.73 kg

Answer:
- The mass of the other ball is approximately 1.73 kg.