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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

Respuesta :

Answer:

[tex]m({v_1}} - {v_2})i[/tex]

Explanation:

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

[tex]P = m *v[/tex]

where m = mass and v =velocity

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

[tex]P_1i = (m*v_1)i[/tex]

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

[tex]P_2i = -(m*v_2)i[/tex]

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:

[tex]P = P_1i + P_2i[/tex]

[tex]P = mv_1i + (-mv_2i)\\\\\\P = mv_1i - mv_2i\\\\\\P = m(v_1 - v_2)i[/tex]

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

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