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14 February, 13:22

9. In the sun devil football game, a receiver, who is standing still, has caught a pass from the quarterback. Before he can move, a tackler, running at a velocity of + 6.89 m/s, grabs him. The tackler holds onto the receiver, and the two head off with a velocity of + 4.78 m/s. The mass of the tackler is 156 kg. Ignoring any frictional forces, what is the mass of the receiver?

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  1. 14 February, 13:28
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    The mass of the receiver is 68.862 kg

    Explanation:

    Given;

    let mass of the receiver be "m₁"

    initial velocity of the receiver, u₁ = 0

    mass of the tackler, m₂ = 156 kg

    initial velocity of the tackler, u₂ = 6.89 m/s

    their final velocity, v = 4.78 m/s

    Apply the principle of conservation of linear momentum, for inelastic collision;

    m₁u₁ + m₂u₂ = v (m₁ + m₂)

    (m₁ x 0) + (156 x 6.89) = 4.78 (m₁ + 156)

    0 + 1074.84 = 4.78 (m₁ + 156)

    1074.84 = 4.78 (m₁ + 156)

    m₁ + 156 = 1074.84 / 4.78

    m₁ + 156 = 224.862

    m₁ = 224.862 - 156

    m₁ = 68.862 kg

    Therefore, the mass of the receiver is 68.862 kg
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