Question

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

Answer 1

`m({v_1}} - {v_2})i`

Step-by-step explanation:

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

`P = m *v`

where m = mass and v =velocity

Given that for the first ball of mass m, the initial velocity in the positive x direction is
`v_1i`, the horizontal component of the initial momentum is given as:

`P_1i = (m*v_1)i`

Also, given that for the second ball of mass m, the initial velocity in the negative x direction is
`v_2i`, the horizontal component of the initial momentum is given as:

`P_2i = -(m*v_2)i`

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:

`P = P_1i + P_2i`

`P = mv_1i + (-mv_2i)\\\\\\P = mv_1i - mv_2i\\\\\\P = m(v_1 - v_2)i`

The total horizontal component of the system's initial momentum is expressed as
`m({v_1}} - {v_2})i`