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  

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form