Understanding Momentum: Solving a Billiard Ball Collision

How can we determine the post-collision velocity of the first billiard ball?

Given the initial velocities and final velocity after a head-on collision, what formula can we use to find the post-collision velocity of the first billiard ball?

Answer:

The post-collision velocity of the first billiard ball can be determined using the law of conservation of momentum.

Velocity is a vector quantity that describes an object's speed and direction of motion. In the scenario of a billiard ball collision, we can apply the law of conservation of momentum, which states that the total momentum of an isolated system remains constant.

The momentum of an object is defined as the product of its mass and velocity: p = m * v. The total initial momentum of the system is the sum of the momenta of the two billiard balls before the collision: p_initial = m * v1 + m * v2.

After the collision, the first billiard ball will rebound with a velocity v1', and the second billiard ball will rebound with a velocity v2'. The total final momentum of the system is the sum of the momenta of the two billiard balls after the collision: p_final = m * v1' + m * v2'.

Since the law of conservation of momentum applies, we can set the initial momentum equal to the final momentum: p_initial = p_final. By simplifying the equation, we get: v1' = v1 + (v2' - v2).

By substituting the given values of initial velocities and final velocity after the collision, we can calculate the post-collision velocity of the first billiard ball: v1' = 154 cm/s + (72 cm/s - (-46 cm/s)) = 272 cm/s.

Understanding the concept of momentum and applying the law of conservation of momentum helps us solve problems related to collisions and post-collision velocities in physics.