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30 July, 09:18

A billiard ball with a mass of 1.5kg is moving at 25m/s and strikes a second ball with a mass of 2.3 kg that is motionless. Find the velocity of the second ball if the first ball stops when it strikes the second ball.

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  1. 30 July, 09:44
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    The velocity of the second ball after the collision will be 16.3 m/s.

    Step-by-Step Explanation:

    Law of conservation of momentum states that the total momentum of an isolated remains the same before and after the collision.

    Let: mass of the first ball = m1 = 1.5 kg

    mass of the second ball = m2 = 2.3 kg

    Momentum before the collision:

    velocity of the first ball = v1 = 25 m/s

    velocity of the second ball = v2 = 0 m/s

    [tex] Initial momentum = m1v1 + m2v2 = 1.5*25 + 2.3*0 = 37.5 kgm/s [/tex]

    Momentum after the collision:

    velocity of the first ball = v1 = 0 m/s

    velocity of the second ball = v2 = x

    [tex]momentum after the collision = m1v1 + m2v2 = 1.5*0 + 2.3*x = 2.3*x[/tex]

    According to law of conservation of momentum:

    Initial momentum = Momentum after collision

    37.5 = 2.3*x

    ⇒ x = 37.5/2.3

    x = 16.3 m/s
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