A 58 g firecracker is at rest at the origin when it explodes into three pieces. The first, with mass 12 g , moves along the x axis at 37 m/s

Question

A 58 g firecracker is at rest at the origin when it explodes into three pieces. The first, with mass 12 g , moves along the x axis at 37 m/s in the positive direction. The second, with mass 22 g , moves along the y axis at 34 m/s in the positive direction. Find the velocity of third piece.

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Euphemia 6 months 2021-08-11T00:07:32+00:00 1 Answers 2 views 0

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    2021-08-11T00:09:12+00:00

    Answer:

    Explanation:

    We shall apply conservation of momentum law in vector form to solve the problem .

    Initial momentum = 0

    momentum of 12 g piece

    = .012 x 37 i since it moves along x axis .

    = .444 i

    momentum of 22 g

    = .022 x 34 j

    = .748 j

    Let momentum of third piece = p

    total momentum

    = p + .444 i + .748 j

    so

    applying conservation law of momentum

    p + .444 i + .748 j  = 0

    p = – .444 i –  .748 j  

    magnitude of p

    = √ ( .444² + .748² )

    = .87 kg m /s

    mass of third piece = 58 – ( 12 + 22 )

    = 24 g = .024 kg

    if v be its velocity

    .024 v = .87

    v = 36.25 m / s .

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