Physics

To solve this problem, we will use the principles of conservation of momentum and conservation of kinetic energy, since the collision is elastic.

 

Given:

Mass of ball 1:

Mass of ball 2:

Initial velocity of ball 1:

Initial velocity of ball 2:

Final velocity of ball 1: (unknown)

Final velocity of ball 2: (unknown)

 

Use the conservation of momentum.

The total momentum before the collision equals the total momentum after the collision:

 

Substitute the known values:

 

Use the conservation of kinetic energy.

The total kinetic energy before the collision equals the total kinetic energy after the collision:

 

Substitute the known values:

 

Solve the system of equations.

Now, we have two equations:

1.

2.

 

From Equation (1), solve for in terms of :

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