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 (-47 m/s) and a second piece, also of mass m, moves with velocity (-47 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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Hải Đăng 2 months 2021-07-24T04:54:44+00:00 1 Answers 2 views 0

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    2021-07-24T04:55:53+00:00

    Answer:

    a) 22.06m/s

    b)45°

    Explanation:

    Let ‘m’ be  mass of 1st and 2nd pieces

    mass of 3rd piece=3m

    v_{1}=velocity of 1st piece
    = -47iˆ  m/s

    v_{2}=velocity of 2nd piece
    = -47jˆ  m/s

    v_{3}=velocity of 3rd piece=?

    By considering conservation of linear momentum, we have

    mv_{1} + mv_{2} + 3mv_{3}=0

    v_{1} + v_{2} + 3v_{3}=0

    3v_{3}= – (v_{1} + v_{2} )

    v_{3} = –\frac{1}{3} (v_{1} + v_{2} )

    Substituting the values of v_{1} and v_{2} in above equation

    v_{3} = –\frac{1}{3} (-47iˆ
    -47jˆ
    ) => 15.6iˆ
    + 15.6jˆ

    (a)Magnitude of the velocity of  the third piece is given by

    |v_{3}| =√15.6²+15.6² => 22.06m/s

    (b) its direction (as an angle relative to the +x axis)  ‘θ’

    θ= tan^{-1} (\frac{15.6}{15.6} ) => tan^{-1} (1 ) =>45°

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