A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves

Question

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-29 m/s) and a second piece, also of mass m, moves with velocity (-29 m/s) . The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the +x axis) of the velocity of the third piece?

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Sigridomena 4 years 2021-08-06T21:27:16+00:00 1 Answers 25 views 0

Answers ( )

  1. huyenthanh
    0
    2021-08-06T21:28:18+00:00
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    Answer with Explanation:

    We are given that

    m_1=m_2=m

    v_1=-29 im/s

    v_2=-29 jm/s

    m_3=3m

    a.Initial velocity of vessel,u=0

    According to law of conservation of momentum

    Mu=m_1v_1+m_2v_2+m_3v_3

    Where M=Mass of  vessel

    0=m(-29i)+m(-29j)+3mv_3

    29im+29jm=3mv_3

    v_3=29i+29jm/s

    Magnitude,\mid v_3\mid=\sqrt{(29)^2+(29)^2}=29\sqrt 2m/s

    b.\theta=tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{29}{29})=45^{\circ}

    Hence, direction of the velocity of third piece=45 degree

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