Two billiard balls with the same mass m move towards one another. Ball one moves in the positive x-direction with a speed of v1i, and ball two moves in the negative x-direction with a speed of v2i. The two balls collide elastically, and both balls change direction after the collision.

Write an expression for the horizontal component of the system's initial momentum

Explanation:

Momentum is the product of a body's mass and its velocity. Mathematically:

where m = mass and v =velocity

Given that for the first ball of mass m, the initial velocity in the positive x direction is , the horizontal component of the initial momentum is given as:

Also, given that for the second ball of mass m, the initial velocity in the negative x direction is , the horizontal component of the initial momentum is given as:

The negative sign is present because the ball is moving in the negative x direction.

Hence, the total horizontal component of the system's initial momentum will be:

The total horizontal component of the system's initial momentum is expressed as