1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Final Exam Review: Motion of an Airplane

  1. May 5, 2012 #1
    This is a question from an old test that I took this semester. My grader did not input anything, so I am left to trying to figure out by myself if my answers are correct or not.


    The motion of an airplane leaving from miami can be described using a cartesian coordinate system with due East coincendet with the positive x-direction and due Noth with the positrive y-direction. The position vector r of the airplane as a function of time from take-off can then be written as:

    vector r = at(i) + (Bt - yt^3)(j)

    [a.] What are the units of the three constants?

    This one was relatively simple. I found that the units were: a = m/s. B = m/s. and y = m/s^3.

    [b.] Find the time(s) when the motion of the airplane is due NE.

    By motion I am guessing they mean velocity,

    So Vx = a and Vy = B - 3yt^2.

    Because it is exactly NE, these two components should be equal to one another, giving Vx = Vy

    ∴ a = B - 3yt^2,

    t = [(a - B)/3y]^1/2.

    The negative answer for t can be discarded.

    [c.] Find the plane's position when the motion is due NE.

    Position means the angle.

    So theta = tan^-1(ry/rx)

    Which is tan^-1([Bt - yt^3]/at)


    Please help me confirm whether I am wrong or right as my final is on Monday and I need to do extremely well in order to pass this course

  2. jcsd
  3. May 6, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I would have thought position meant position in 2 dimensions, probably in Cartesian co-ordinates.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook