An airplane flies with an unknown velocity due east. The plane is experiencing wind of 12 m/s due north which produces a resulta

Question

An airplane flies with an unknown velocity due east. The plane
is experiencing wind of 12 m/s due north which produces a
resultant velocity of 35.11 m/s northeast. Determine the
unknown velocity produced by the plane engines.

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Kim Cúc 6 months 2021-07-15T19:30:46+00:00 2 Answers 20 views 0

Answers ( )

    0
    2021-07-15T19:32:29+00:00

    Answer:

    The unknown velocity produced by the planes engines is approximately 33 m/s due east

    Explanation:

    The given parameters are;

    The direction of the airplane’s flight = East ward

    The speed of the wind experienced by the plane = 12 m/s

    The direction of the wind = Due north

    The resultant velocity of the = 35.11 m/s northeast

    Let the velocity of the plane be v_p

    We present the velocity of the plane and the velocity of the wind vectorially as follows;

    Velocity of the plane = v_p·\hat i

    The velocity of the wind =v_w· \hat j = 12·\hat j

    The resultant velocity, v_r of the airplane is given by the following relation from Pythagoras’s theorem for right triangles;

    v_r = √((v_p)² + (v_w)²)

    Therefore;

    35.11 = √((v_p)² + (12)²)

    v_p = √(35.11² – 12²) = 32.9956375904 ≈ 33 m/s

    Therefore;

    The velocity of the airplane = 33 m/s due east

    The unknown velocity produced by the planes engines ≈ 33 m/s due east

    0
    2021-07-15T19:32:33+00:00

    Answer:

    32.99m/s

    Explanation:

    Using the formula for calculating the resultant velocity according to Pythagoras theorem

    R² = 12²+x²

    35.11² = 12²+x²

    X² = 35.11²-12²

    X² = 1232.7121-144

    X² = 1088.8121

    X = √1088.8121

    X = 32.99m/s

    Hence the unknown velocity produced by the plane engines is 32.99m/s

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