physics

A 48-kg girl stands on a 8-kg wagon holding two 19.5-kg weights. She throws the weights horizontally off the back of the wagon at a speed of 9.0 m/s relative to herself. Assuming that the wagon was at rest initially, what is the speed with which the girl will move after she throws the weights one at a time, each with a speed of 9.0 m/s relative to herself?

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  1. Weight number 1:
    48 + 8 + 19.5 = 75.5 kg on the wagon
    19.5 kg back at 9 relative to ground and girl
    so
    75.5 u = 19.5 * 9
    u = 2.325 forward
    now
    weight number 2
    before throw:
    momentum = 75.5 * 2.325 = 175.5
    relative to ground
    after throw
    missile momentum back relative to ground
    = 19.5 (9 -2.325 ) = 130 kg m/s back
    cart and girl mass = 48+8 = 56 kg
    so
    56 v - 130 = momentum after
    so
    56 v - 130 = 175.5
    56 v = 305.5
    v = 5.46 meters/second

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