physics

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A man of mass 70 kg and a boy of mass 30 kg dive of the end of a boat, of mass 150 kg with a horizontal velocity of 2 m/s relativeto the boat. if initially the boat is at rest, findits velocity just after (1) both the man and boy dive off simultaneously (2) the man dives of first followed by the boy

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    Conserve momentum. (Initial = final)

    (1) Man and boy simultaneously jump and push the boat back.
    m1 = mass of man
    m2 = mass of boy
    v1 = velocity of man (and boy)
    m3 = mass of boat
    v3 =
    0 = (m1+m2) v1 + m3 v3
    Rearrange:
    v3 = - (m1+m2) v1 / m3
    = - 100 * 2 / 150
    = 1.33 m/s

    (2) First, the man pushes back the boat and the boy, then the boy further pushes back the boat.

    Key point: When the boy jumps off at v1 _relative_ to the boat, the boat is not at rest.

    m1 = mass of man
    m2 = mass of boy
    v1 = velocity of man
    v2 = intermediate velocity of boat
    m3 = mass of boat
    v4 = final velocity of boat

    First jump:
    0 = m1 v1 + (m2+m3) v2
    Second jump:
    (m2+m3) v2 = m2 (v2+v1) + m3 v4

    Rearrange:
    v2 = - m1 v1 / (m2+m3)
    v4 = v2 - (m2 v1)/ m3

    Substitute first into the second
    v4 = - (m1/(m2+m3)+m2/m3) v1

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