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13 December, 09:54

A 2.90-kg ball, moving to the right at a velocity of 4.69 m/s on a frictionless table, collides head-on with a stationary 8.80-kg ball. find the final velocities of (a) the 2.90-kg ball and of (b) the 8.80-kg ball if the collision is elastic. (c) find the magnitude and direction of the final velocity of the two balls if the collision is completely inelastic.

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  1. 13 December, 13:00
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    Elastic collision:

    momentum initial = momentum final

    Kinetic energy is conserved

    2.90-kg ball,

    Since kinetic energy is conserved, velocity transferred to other ball so final velocity is v₁ = 0 m/s

    8.80 kg ball

    Since kinetic energy is conserved, velocity transferred to this ball so final velocity is v₂ = 4.69 m/s right

    For perfectly inelastic, masses are combined and they stick together. One final velocity, v

    m₁ = 2.90 kg

    v₁ᵢ = 4.69 m/s right

    m₂ = 8.80 kg

    v₂ᵢ = 0 m/s

    v = ? m/s

    Momentum is conserved

    m₁v₁ᵢ + m₂v₂ᵢ = v (m₁ + m₂)

    v = (m₁v₁ᵢ + m₂v₂) / (m₁ + m₂)

    v = (2.90 kg * 4.69 m/s + 0) / (2.90 kg + 8.80 kg)

    v = 1.16 m/s
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