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18 September, 06:07

A spaceship of mass 2.0*106 kg is cruising at a speed of 5.0*106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.0*105 kg, is blown straight backward with a speed of 2.0*106 m/s. A sec-ond piece, with mass 8.0*105 kg, continues forward at 1.0*106 m/s. What are the direction and speed of the third piece?

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  1. 18 September, 06:25
    0
    v3 = 1.6*10^7 m/s

    and the directio is straight forward

    Explanation:

    Given that,

    spaceship of mass M = 2.0*10^6kg

    the velocity is V = 5.0*10^6m/s

    one section:

    mass of m1 = 5.0*10^5kg,

    speed v1 = - 2.0*10^6m/s

    sec-ond

    mass, m2 = 8.0*10^5kg,

    speed, v2 = 1.0*10^6m/s

    use conservation of momentum

    Initial momentum = final momentum

    M*vi = m1*v1+m2*v2+m3*v3

    (2*10^6) * (5*10^6) = (5.0*10^5) * (-2*10^6) + (8.0*10^5) * (1*10^6) + (2*10^6 - 5.0*10^5 - 8.0*10^5) * v3

    (10*10^12) = - 10*10^11 + 9.0*10^11 + (7.0*10^5) * v3

    v3 = 1.6*10^7 m/s
  2. 18 September, 06:26
    0
    Answer: v3 = 1.6*10^7 m/s, and the direction is the same as the initial direction of movement of the spaceship

    Explanation:

    The initial mass is M = 2.0*10^6kg

    the velocity is V = 5.0*10^6m/s

    then, the initial moment is P = M*V = 1.0*10^13m*kg/s

    now, we must have that the momentum before and afther must be equal, after we have:

    one part with:

    m1 = 5.0*10^5kg, v1 = - 2.0*10^6m/s

    then p1 = - 1.0*10^12kh*m/s

    other part has:

    m2 = 8.0*10^5kg, v2 = 1.0*10^6m/s

    p2 = 8*10^11kg*m/s

    then, the third object must have a momentum:

    p3 = P - p1 - p2 = 10.0*10^12 - 0.8*10^12 + 2.0*10^12 = 11.2*10^12

    then m3*v3 = 11.2*10^12 kg*m/s so from this we know that the velocity is in the same direction than the initial velocity.

    now, we can find m3 by:

    M = m1 + m2 + m3

    m3 = M - m1 - m2 = 2.0*10^6kg - 0.5*10^6kg - 0.8*10^6kg = 0.7*10^6kg

    then v3 = (11.2*10^12) / (07*10^6) m/s = (11.2/0.7) * 10^ (12 - 6) m/s = 16.0*10^6 m/s

    v3 = 1.6*10^7 m/s
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