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19 January, 19:59

During a football game, a receiver has just caught a pass and is standing still. Before he can move, a tackler, running at a velocity of 2.60 m/s, grabs and holds onto him so that they move off together with a velocity of 1.30 m/s. If the mass of the tackler is 122 kg, determine the mass of the receiver. Assume momentum is conserved.

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  1. 19 January, 21:59
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    122kg

    Explanation:

    Using the law of conservation of momentum which states that 'the sum of momentum of bodies before collision is equal to their sum after collision. The bodies will move together with a common velocity after collision.

    Momentum = Mass * Velocity

    Before collision;

    Momentum of receiver m1u1 = 0 kgm/s (since the receiver is standing still)

    Momentum of the tackler

    m2u2 = 2.60*122 = 317.2 kgm/s

    where m2 and u2 are the mass and velocity of the tacker respectively.

    Sum of momentum before collision = 0+317.2 = 317.2 kgm/s

    After collision

    Momentum of the bodies = (m1+m2) v

    v = their common velocity

    m1 = mass of the receiver

    Momentum of the bodies = (122+m1) (1.30)

    Momentum of the bodies = 158.6+1.30m1

    According to the law above;

    317.2 = 158.6+1.30m1

    317.2-158.6 = 1.30m1

    158.6 = 1.30m1

    m1 = 158.6/1.30

    m1 = 122kg

    The mas of the receiver is 122kg
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