Billiard Ball Collision Problem: Solution and Explanation

What is the final velocity of the green billiard ball after the collision?

In an elastic collision between a 3.1 kg blue billiard ball and an initially stationary green billiard ball of identical mass, the final velocity of the green ball is -1.0 m/s.

Answer:

The final velocity of the green billiard ball after the collision is -1.0 m/s.

In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. This principle is based on the conservation of momentum. The given problem involves a 3.1 kg blue billiard ball moving at 3.1 m/s before the collision and a green billiard ball of identical mass initially at rest. After the collision, the blue billiard ball is traveling at -7.0 m/s. We can apply the concept of conservation of momentum to determine the final velocity of the green billiard ball.

Using the equation: m1 * v1 + m2 * v2 = m1 * u1 + m2 * u2 where m1 and m2 are the masses of the blue and green billiard balls, v1 and v2 are their final velocities, and u1 and u2 are their initial velocities.

Plugging in the given values, we have: (3.1 kg * 3.1 m/s) + (3.1 kg * 0 m/s) = (3.1 kg * -7.0 m/s) + (3.1 kg * v2)

Simplifying the equation, we find: -9.61 kg * m/s = 9.61 kg * v2

Dividing both sides by 9.61 kg, we get: v2 = -1.0 m/s

Therefore, the green billiard ball is moving at a velocity of -1.0 m/s after the collision. This solution demonstrates the application of conservation of momentum in elastic collisions.