Math (pre calc)

posted by Sarah

You have recently been promoted and are now a senior pilot with BHS Exprress, providing courteous and timely service to countless cities across the Northeast. In order to arrive in New York City at the scheduled time, you know you must fly at a speed of 380mph on a course of 160 degrees. You check the weather conditions and find that the wind is blowing at 42 mph from 35 degrees East of North. Find the following information: Eastern Component of the Air velocity, southern component of the air velocity, air speed, heading. I have already solved for the velocities so I just need air speed and heading

  1. Steve

    can you convert those speeds and headings to vectors? That's the first step in all these problems. If not, it's time for review. If so, what do you get?

  2. Henry

    1. Vw = 42mi/h[35o]E. of N.
    X = 42*sin35 = 24.1mi/h = E. component.
    Y = 42*Cos35 = 34.4mi/h = S. component.

    2. 380mi/h[160o] Bearing.
    X = 380*sin160 = 130mi/h.
    Y = 380*Cos160 = -357mi/h.

    Add the components of the wind and plane:
    X = 24.1 + 130 = 154.1 mi/h.
    Y = 34.4 + (-357) = -322.7 mi/h.

    X + Yi = 154.1-322.7i = 358 mi/h[154.5o].

    Tan(A) = (-322.7)/154.1 = -2.09409,
    A = -64.5o = 64.5o S. of E. = 154.5o CW from +Y-axis. = Direction.

  3. Sarah

    Okay so for the heading I got 334.474 degrees south of east but I'm confused on the air speed. We only did this for two days in class so I'm very confused on the vector unit, which is why I'm having so much trouble. It's break now and my teacher won't answer any questions.

  4. Henry

    Sarah, it is impossible to have 334o South of East. 334o CW from the +Y-axis is possible. 334o CCW from the +X-axis is also possible.

    I would like to see your calculations.

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