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Final Exam Review: Motion of an Airplane 
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#1
May512, 11:11 PM

P: 21

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.
Question: The motion of an airplane leaving from miami can be described using a cartesian coordinate system with due East coincendet with the positive xdirection and due Noth with the positrive ydirection. The position vector r of the airplane as a function of time from takeoff 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 Thanks. 


#2
May612, 02:26 AM

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